
X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
1 
1.2807 
1.61515 
1.97712 
2.31978 
1.28403 
1.64329 
2.07244 
2.5378 
2.97865 
1.64872 
2.10984 
2.66083 
3.25846 
3.82467 
2.117 
2.70973 
3.4174 
4.18446 
4.91097 
2.71828 
3.48129 
4.39042 
5.37436 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.38482
-5.28966
-9.19889
-13.1081
-17.0174
-20.9266
-24.8358
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
1 
1.13278 
1.2807 
1.44235 
1.61515 
1.79517 
1.97712 
2.15447 
2.31978 
1.13315 
1.2835 
1.45105 
1.63418 
1.82999 
2.03401 
2.24024 
2.44128 
2.62865 
1.28403 
1.45434 
1.64415 
1.85165 
2.07352 
2.30472 
2.53845 
2.76629 
2.97865 
1.45499 
1.64796 
1.86302 
2.09814 
2.34955 
2.61155 
2.87641 
3.13461 
3.37526 
1.64872 
1.86739 
2.11108 
2.37751 
2.6624 
2.95927 
3.2594 
3.55197 
3.82467 
1.86825 
2.11606 
2.39222 
2.69413 
3.01695 
3.35335 
3.69342 
4.02494 
4.33391 
2.117 
2.39786 
2.71085 
3.05298 
3.41879 
3.79996 
4.18528 
4.56089 
4.91097 
2.39888 
2.71724 
3.07197 
3.4597 
3.87422 
4.30612 
4.74268 
5.16823 
5.56486 
2.71828 
3.07922 
3.48129 
3.92071 
4.39042 
4.87977 
5.37436 
5.85645 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.84137
-4.12667
-7.27439
-10.4508
-13.5944
-16.7469
-19.9062
-23.0686
-26.2323
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
1 
1.06445 
1.13278 
1.20491 
1.2807 
1.35994 
1.44235 
1.52757 
1.61515 
1.70455 
1.79517 
1.88628 
1.97712 
2.06681 
2.15447 
2.23912 
2.31978 
1.06449 
1.13309 
1.20582 
1.2826 
1.36327 
1.44762 
1.53534 
1.62606 
1.71929 
1.81446 
1.91092 
2.00791 
2.10461 
2.2001 
2.29341 
2.38352 
2.46939 
1.13315 
1.20617 
1.28358 
1.3653 
1.45118 
1.54096 
1.63434 
1.73091 
1.83015 
1.93146 
2.03414 
2.1374 
2.24033 
2.34199 
2.44132 
2.53725 
2.62865 
1.20623 
1.28395 
1.36636 
1.45335 
1.54475 
1.64033 
1.73973 
1.84252 
1.94816 
2.05601 
2.16532 
2.27523 
2.38481 
2.49302 
2.59876 
2.70088 
2.79818 
1.28403 
1.36676 
1.45447 
1.54707 
1.64437 
1.74611 
1.85192 
1.96134 
2.0738 
2.1886 
2.30496 
2.42197 
2.53861 
2.6538 
2.76637 
2.87507 
2.97865 
1.36684 
1.45491 
1.54828 
1.64684 
1.75042 
1.85872 
1.97135 
2.08783 
2.20754 
2.32975 
2.45361 
2.57816 
2.70233 
2.82496 
2.94478 
3.0605 
3.17076 
1.45499 
1.54874 
1.64813 
1.75305 
1.86331 
1.97859 
2.09849 
2.22248 
2.34991 
2.48 
2.61185 
2.74444 
2.87662 
3.00715 
3.1347 
3.25788 
3.37526 
1.54883 
1.64862 
1.75442 
1.86611 
1.98348 
2.1062 
2.23383 
2.36581 
2.50146 
2.63994 
2.7803 
2.92144 
3.06214 
3.20109 
3.33687 
3.468 
3.59294 
1.64872 
1.75495 
1.86758 
1.98647 
2.1114 
2.24204 
2.3779 
2.5184 
2.66279 
2.81021 
2.95961 
3.10985 
3.25963 
3.40754 
3.55208 
3.69166 
3.82467 
1.75505 
1.86814 
1.98803 
2.11459 
2.24758 
2.38664 
2.53127 
2.68083 
2.83453 
2.99145 
3.1505 
3.31043 
3.46987 
3.62732 
3.78117 
3.92976 
4.07134 
1.86825 
1.98862 
2.11625 
2.25098 
2.39255 
2.54057 
2.69453 
2.85373 
3.01736 
3.1844 
3.3537 
3.52394 
3.69366 
3.86126 
4.02504 
4.1832 
4.33391 
1.98874 
2.11688 
2.25274 
2.39616 
2.54686 
2.70444 
2.86832 
3.0378 
3.21197 
3.38979 
3.57 
3.75122 
3.93189 
4.1103 
4.28464 
4.453 
4.61343 
2.117 
2.25341 
2.39804 
2.55071 
2.71114 
2.87888 
3.05333 
3.23374 
3.41915 
3.60843 
3.80026 
3.99317 
4.18548 
4.3754 
4.56098 
4.7402 
4.91097 
2.25353 
2.39875 
2.55271 
2.71523 
2.88601 
3.06457 
3.25028 
3.44232 
3.63969 
3.84117 
4.04538 
4.25073 
4.45544 
4.6576 
4.85514 
5.04592 
5.2277 
2.39888 
2.55346 
2.71736 
2.89037 
3.07217 
3.26225 
3.45994 
3.66436 
3.87446 
4.08894 
4.30631 
4.5249 
4.74281 
4.958 
5.16828 
5.37135 
5.56486 
2.55359 
2.71816 
2.89263 
3.07681 
3.27034 
3.47268 
3.68312 
3.90073 
4.12438 
4.35269 
4.58408 
4.81676 
5.04872 
5.27778 
5.50162 
5.71778 
5.92376 
2.71828 
2.89348 
3.07922 
3.27528 
3.48129 
3.69669 
3.92071 
4.15236 
4.39042 
4.63345 
4.87977 
5.12744 
5.37436 
5.61818 
5.85645 
6.08655 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.585913
-3.82864
-6.97844
-10.0314
-13.0161
-15.9987
-18.9919
-21.9933
-25.0007
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
1 
1.03174 
1.06445 
1.09813 
1.13278 
1.16838 
1.20491 
1.24236 
1.2807 
1.3199 
1.35994 
1.40077 
1.44235 
1.48463 
1.52757 
1.57109 
1.61515 
1.65966 
1.70455 
1.74975 
1.79517 
1.84071 
1.88628 
1.93178 
1.97712 
2.02216 
2.06681 
2.11096 
2.15447 
2.19723 
2.23912 
2.28001 
2.31978 
1.03174 
1.06449 
1.09824 
1.13299 
1.16874 
1.20546 
1.24315 
1.28179 
1.32135 
1.3618 
1.4031 
1.44523 
1.48813 
1.53176 
1.57605 
1.62096 
1.66641 
1.71234 
1.75866 
1.80529 
1.85215 
1.89913 
1.94616 
1.9931 
2.03987 
2.08635 
2.13242 
2.17796 
2.22286 
2.26698 
2.31019 
2.35238 
2.39341 
1.06449 
1.09828 
1.1331 
1.16896 
1.20583 
1.24373 
1.28261 
1.32248 
1.36329 
1.40502 
1.44764 
1.4911 
1.53536 
1.58038 
1.62608 
1.67241 
1.71931 
1.76669 
1.81448 
1.86259 
1.91094 
1.95942 
2.00793 
2.05637 
2.10462 
2.15258 
2.20011 
2.2471 
2.29342 
2.33894 
2.38353 
2.42705 
2.46939 
1.09829 
1.13314 
1.16907 
1.20606 
1.24411 
1.2832 
1.32333 
1.36445 
1.40656 
1.44962 
1.49359 
1.53843 
1.5841 
1.63054 
1.67769 
1.7255 
1.77388 
1.82277 
1.87207 
1.92172 
1.97159 
2.02161 
2.07167 
2.12164 
2.17143 
2.22091 
2.26995 
2.31843 
2.36622 
2.41318 
2.45919 
2.5041 
2.54778 
1.13315 
1.16911 
1.20618 
1.24434 
1.2836 
1.32394 
1.36533 
1.40776 
1.45121 
1.49563 
1.541 
1.58726 
1.63438 
1.6823 
1.73095 
1.78027 
1.83019 
1.88063 
1.9315 
1.98271 
2.03418 
2.08578 
2.13743 
2.18899 
2.24036 
2.2914 
2.342 
2.39202 
2.44133 
2.48978 
2.53725 
2.58359 
2.62865 
1.16912 
1.20622 
1.24447 
1.28384 
1.32435 
1.36596 
1.40867 
1.45245 
1.49727 
1.54311 
1.58991 
1.63765 
1.68626 
1.7357 
1.78589 
1.83678 
1.88828 
1.94032 
1.99281 
2.04565 
2.09875 
2.15199 
2.20527 
2.25847 
2.31147 
2.36414 
2.41634 
2.46795 
2.51882 
2.56882 
2.61779 
2.6656 
2.71209 
1.20623 
1.24451 
1.28397 
1.3246 
1.36638 
1.40932 
1.45338 
1.49855 
1.5448 
1.59209 
1.64038 
1.68963 
1.73979 
1.79079 
1.84258 
1.89508 
1.94822 
2.00191 
2.05607 
2.11058 
2.16537 
2.2203 
2.27528 
2.33017 
2.38485 
2.43918 
2.49305 
2.54629 
2.59878 
2.65036 
2.70089 
2.75021 
2.79818 
1.24452 
1.28402 
1.32473 
1.36664 
1.40976 
1.45406 
1.49952 
1.54612 
1.59384 
1.64263 
1.69245 
1.74326 
1.79501 
1.84763 
1.90107 
1.95524 
2.01006 
2.06546 
2.12133 
2.17758 
2.2341 
2.29078 
2.3475 
2.40413 
2.46055 
2.51661 
2.57218 
2.62712 
2.68127 
2.73449 
2.78662 
2.83751 
2.88701 
1.28403 
1.32477 
1.36678 
1.41002 
1.45451 
1.50021 
1.54712 
1.5952 
1.64443 
1.69477 
1.74617 
1.7986 
1.85199 
1.90628 
1.96141 
2.0173 
2.07387 
2.13102 
2.18867 
2.2467 
2.30502 
2.3635 
2.42202 
2.48045 
2.53865 
2.5965 
2.65383 
2.71051 
2.76638 
2.82129 
2.87508 
2.92759 
2.97865 
1.32478 
1.36683 
1.41016 
1.45478 
1.50068 
1.54783 
1.59623 
1.64584 
1.69663 
1.74856 
1.8016 
1.85569 
1.91078 
1.96679 
2.02367 
2.08133 
2.1397 
2.19866 
2.25814 
2.31802 
2.37819 
2.43852 
2.4989 
2.55918 
2.61924 
2.67892 
2.73807 
2.79655 
2.8542 
2.91085 
2.96634 
3.02052 
3.0732 
1.36684 
1.41022 
1.45493 
1.50096 
1.54831 
1.59697 
1.6469 
1.69808 
1.75048 
1.80407 
1.85879 
1.9146 
1.97143 
2.02923 
2.08791 
2.1474 
2.20762 
2.26846 
2.32982 
2.3916 
2.45368 
2.51593 
2.57822 
2.64042 
2.70238 
2.76395 
2.82499 
2.88533 
2.9448 
3.00325 
3.06051 
3.1164 
3.17076 
1.41023 
1.45498 
1.50111 
1.54861 
1.59746 
1.64766 
1.69917 
1.75198 
1.80605 
1.86133 
1.91779 
1.97537 
2.03401 
2.09364 
2.15419 
2.21557 
2.27769 
2.34047 
2.40378 
2.46752 
2.53157 
2.59579 
2.66006 
2.72423 
2.78816 
2.85169 
2.91466 
2.97692 
3.03828 
3.09858 
3.15766 
3.21532 
3.27141 
1.45499 
1.50117 
1.54876 
1.59777 
1.64817 
1.69996 
1.75311 
1.8076 
1.86338 
1.92042 
1.97867 
2.03808 
2.09858 
2.1601 
2.22257 
2.2859 
2.34999 
2.41476 
2.48008 
2.54584 
2.61193 
2.67819 
2.7445 
2.81071 
2.87667 
2.94221 
3.00719 
3.07141 
3.13472 
3.19694 
3.25789 
3.31739 
3.37526 
1.50118 
1.54882 
1.59792 
1.64848 
1.70049 
1.75392 
1.80876 
1.86497 
1.92253 
1.98138 
2.04148 
2.10277 
2.16519 
2.22867 
2.29312 
2.35846 
2.42459 
2.49141 
2.55881 
2.62666 
2.69484 
2.7632 
2.83162 
2.89993 
2.96798 
3.03561 
3.10264 
3.16891 
3.23423 
3.29842 
3.36131 
3.42269 
3.4824 
1.54883 
1.59798 
1.64865 
1.70081 
1.75447 
1.8096 
1.86618 
1.92418 
1.98356 
2.04428 
2.10628 
2.16952 
2.23392 
2.29941 
2.36591 
2.43332 
2.50156 
2.5705 
2.64003 
2.71004 
2.78038 
2.85092 
2.92151 
2.99199 
3.0622 
3.13197 
3.20113 
3.2695 
3.3369 
3.40313 
3.46801 
3.53134 
3.59294 
1.598 
1.64871 
1.70098 
1.7548 
1.81016 
1.86704 
1.92542 
1.98526 
2.04652 
2.10917 
2.17314 
2.23839 
2.30483 
2.3724 
2.44101 
2.51057 
2.58096 
2.65209 
2.72384 
2.79606 
2.86864 
2.94142 
3.01424 
3.08696 
3.1594 
3.23139 
3.30275 
3.37329 
3.44282 
3.51115 
3.57809 
3.64344 
3.70699 
1.64872 
1.70104 
1.75497 
1.81051 
1.86762 
1.92631 
1.98654 
2.04827 
2.11148 
2.17612 
2.24213 
2.30944 
2.378 
2.44771 
2.5185 
2.59026 
2.66289 
2.73628 
2.8103 
2.88482 
2.9597 
3.03479 
3.10993 
3.18495 
3.25969 
3.33397 
3.40759 
3.48037 
3.55211 
3.62261 
3.69167 
3.75909 
3.82467 
1.70106 
1.75504 
1.81068 
1.86798 
1.92691 
1.98746 
2.0496 
2.11329 
2.17851 
2.2452 
2.3133 
2.38275 
2.45348 
2.52541 
2.59844 
2.67248 
2.74742 
2.82314 
2.89951 
2.9764 
3.05365 
3.13112 
3.20865 
3.28605 
3.36317 
3.4398 
3.51576 
3.59085 
3.66486 
3.7376 
3.80886 
3.87842 
3.94607 
1.75505 
1.81075 
1.86816 
1.92727 
1.98807 
2.05054 
2.11466 
2.18038 
2.24766 
2.31647 
2.38673 
2.45839 
2.53137 
2.60558 
2.68093 
2.75732 
2.83464 
2.91276 
2.99155 
3.07088 
3.15058 
3.23052 
3.3105 
3.39037 
3.46993 
3.54899 
3.62736 
3.70483 
3.7812 
3.85625 
3.92977 
4.00153 
4.07134 
1.81077 
1.86823 
1.92746 
1.98845 
2.05118 
2.11564 
2.18178 
2.24959 
2.31901 
2.39 
2.4625 
2.53643 
2.61172 
2.68829 
2.76603 
2.84485 
2.92462 
3.00522 
3.08651 
3.16836 
3.2506 
3.33306 
3.41559 
3.49799 
3.58007 
3.66165 
3.7425 
3.82244 
3.90123 
3.97866 
4.05451 
4.12856 
4.20057 
1.86825 
1.92754 
1.98865 
2.05157 
2.1163 
2.18279 
2.25104 
2.321 
2.39263 
2.46587 
2.54067 
2.61695 
2.69463 
2.77362 
2.85384 
2.93515 
3.01746 
3.10062 
3.18449 
3.26893 
3.35378 
3.43887 
3.52401 
3.60903 
3.69372 
3.77788 
3.8613 
3.94377 
4.02507 
4.10496 
4.18322 
4.25961 
4.33391 
1.92755 
1.98872 
2.05177 
2.1167 
2.18347 
2.25209 
2.3225 
2.39468 
2.46858 
2.54415 
2.62132 
2.70002 
2.78017 
2.86167 
2.94443 
3.02833 
3.11324 
3.19904 
3.28558 
3.3727 
3.46024 
3.54803 
3.63588 
3.72359 
3.81097 
3.8978 
3.98388 
4.06896 
4.15284 
4.23526 
4.31601 
4.39483 
4.47149 
1.98874 
2.05185 
2.11691 
2.18389 
2.25279 
2.32357 
2.39622 
2.4707 
2.54694 
2.62491 
2.70453 
2.78573 
2.86842 
2.95251 
3.0379 
3.12446 
3.21207 
3.30059 
3.38988 
3.47976 
3.57009 
3.66066 
3.75129 
3.84179 
3.93194 
4.02153 
4.11034 
4.19813 
4.28466 
4.3697 
4.45301 
4.53433 
4.61343 
2.05187 
2.11698 
2.1841 
2.25321 
2.3243 
2.39733 
2.47229 
2.54913 
2.62779 
2.70823 
2.79038 
2.87416 
2.95948 
3.04624 
3.13433 
3.22364 
3.31403 
3.40537 
3.49749 
3.59023 
3.68341 
3.77686 
3.87037 
3.96374 
4.05676 
4.14919 
4.24082 
4.33139 
4.42067 
4.50841 
4.59436 
4.67827 
4.75987 
2.117 
2.18419 
2.25344 
2.32474 
2.39808 
2.47344 
2.55077 
2.63005 
2.71121 
2.7942 
2.87896 
2.9654 
3.05342 
3.14294 
3.23383 
3.32597 
3.41923 
3.51347 
3.60851 
3.70419 
3.80034 
3.89675 
3.99324 
4.08957 
4.18554 
4.2809 
4.37543 
4.46888 
4.561 
4.65153 
4.74021 
4.82677 
4.91097 
2.1842 
2.25352 
2.32497 
2.39854 
2.47421 
2.55195 
2.63174 
2.71353 
2.79728 
2.8829 
2.97035 
3.05953 
3.15035 
3.24271 
3.33648 
3.43155 
3.52778 
3.625 
3.72306 
3.82178 
3.92098 
4.02045 
4.12 
4.21939 
4.3184 
4.4168 
4.51433 
4.61074 
4.70578 
4.79918 
4.89068 
4.97999 
5.06686 
2.25353 
2.32505 
2.39877 
2.47467 
2.55275 
2.63296 
2.71528 
2.79967 
2.88607 
2.97442 
3.06464 
3.15665 
3.25036 
3.34565 
3.4424 
3.54049 
3.63976 
3.74007 
3.84124 
3.9431 
4.04545 
4.14808 
4.25078 
4.35333 
4.45548 
4.557 
4.65763 
4.7571 
4.85516 
4.95153 
5.04592 
5.13807 
5.2277 
2.32507 
2.39886 
2.47492 
2.55323 
2.63378 
2.71654 
2.80148 
2.88855 
2.97769 
3.06884 
3.16193 
3.25686 
3.35354 
3.45185 
3.55168 
3.65288 
3.7553 
3.8588 
3.96318 
4.06827 
4.17387 
4.27976 
4.38572 
4.49152 
4.59692 
4.70166 
4.80548 
4.90811 
5.00928 
5.10871 
5.2061 
5.30117 
5.39364 
2.39888 
2.47501 
2.55348 
2.63428 
2.71739 
2.80278 
2.89041 
2.98024 
3.07221 
3.16626 
3.2623 
3.36025 
3.45999 
3.56143 
3.66442 
3.76884 
3.87451 
3.98129 
4.08899 
4.19742 
4.30636 
4.41561 
4.52494 
4.6341 
4.74284 
4.85091 
4.95802 
5.06391 
5.16829 
5.27087 
5.37136 
5.46945 
5.56486 
2.47502 
2.55357 
2.63454 
2.7179 
2.80365 
2.89175 
2.98217 
3.07485 
3.16974 
3.26677 
3.36586 
3.46692 
3.56983 
3.67448 
3.78075 
3.88848 
3.99751 
4.10768 
4.21879 
4.33066 
4.44306 
4.55578 
4.66858 
4.7812 
4.8934 
5.00489 
5.11541 
5.22466 
5.33235 
5.43819 
5.54186 
5.64307 
5.7415 
2.55359 
2.63463 
2.71817 
2.80418 
2.89265 
2.98355 
3.07683 
3.17246 
3.27036 
3.37048 
3.47271 
3.57697 
3.68315 
3.79113 
3.90077 
4.01191 
4.12441 
4.23807 
4.35272 
4.46813 
4.58411 
4.7004 
4.81678 
4.93298 
5.04873 
5.16377 
5.27779 
5.39051 
5.50162 
5.61082 
5.71778 
5.8222 
5.92376 
2.63465 
2.71827 
2.80445 
2.8932 
2.98447 
3.07826 
3.17451 
3.27317 
3.37418 
3.47747 
3.58295 
3.69052 
3.80008 
3.91148 
4.0246 
4.13927 
4.25534 
4.37261 
4.49089 
4.60997 
4.72963 
4.84961 
4.96968 
5.08957 
5.209 
5.32769 
5.44533 
5.56163 
5.67626 
5.78892 
5.89928 
6.00702 
6.1118 
2.71828 
2.80456 
2.89348 
2.98504 
3.07922 
3.17598 
3.27528 
3.37707 
3.48129 
3.58786 
3.69669 
3.80768 
3.92071 
4.03565 
4.15236 
4.27067 
4.39042 
4.51142 
4.63345 
4.75631 
4.87977 
5.00356 
5.12744 
5.25114 
5.37436 
5.49681 
5.61818 
5.73817 
5.85645 
5.97269 
6.08655 
6.1977 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.460196
-3.67909
-6.83888
-9.91509
-12.8798
-15.8286
-18.7802
-21.7386
-24.7029
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd1.png');
clf
figure(2);
saveas(gcf,'oneResidualInd1.png');

N = [
4
8
16
32
];
E = [
-8.89932
-10.8628
-12.827
-14.8237
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.9e-05
0.000339
0.007632
0.348135
];
T2 = [
0.000806
0.010013
0.102916
1.21661
];
figure(4);
subplot(3,1,1);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0 
0.222725 
0.533126 
0.882143 
1.20738 
0.221869 
0.566754 
0.982752 
1.44106 
1.88353 
0.556483 
1.01351 
1.55737 
2.15127 
2.72381 
1.0075 
1.59663 
2.29677 
3.05676 
3.78362 
1.60338 
2.35536 
3.25216 
4.2187 
5.10873 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
1.13533
0.660625
0.354927
0.0952196
-0.152324
-0.396566
-0.639884
-0.882935
-1.12591
-1.36886
-1.6118
-1.85474
-2.09768
-2.34062
-2.58356
-2.82649
-3.06943
-3.31237
-3.55531
-3.79825
-4.04119
-4.28413
-4.52707
-4.77001
-5.01295
-5.25588
-5.49882
-5.74176
-5.9847
-6.22764
-6.47058
-6.71352
-6.95646
-7.1994
-7.44233
-7.68527
-7.92821
-8.17115
-8.41409
-8.65703
-8.89997
-9.14291
-9.38585
-9.62879
-9.87172
-10.1147
-10.3576
-10.6005
-10.8435
-11.0864
-11.3294
-11.5723
-11.8152
-12.0582
-12.3011
-12.5441
-12.787
-13.0299
-13.2729
-13.5158
-13.7587
-14.0017
-14.2446
-14.4876
-14.7305
-14.9734
-15.2164
-15.4593
-15.7023
-15.9452
-16.1881
-16.4311
-16.674
-16.917
-17.1599
-17.4028
-17.6458
-17.8887
-18.1316
-18.3746
-18.6175
-18.8605
-19.1034
-19.3463
-19.5893
-19.8322
-20.0752
-20.3181
-20.561
-20.804
-21.0469
-21.2899
-21.5328
-21.7757
-22.0187
-22.2616
-22.5045
-22.7475
-22.9904
-23.2334
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0 
0.12729 
0.272986 
0.433658 
0.606113 
0.786161 
0.968272 
1.14547 
1.30898 
0.127123 
0.276144 
0.442507 
0.624959 
0.820497 
1.02457 
1.23106 
1.43244 
1.62036 
0.274904 
0.444956 
0.634294 
0.841467 
1.06326 
1.29465 
1.52883 
1.75743 
1.97101 
0.443713 
0.636749 
0.851705 
1.08675 
1.33825 
1.60056 
1.86605 
2.12526 
2.36743 
0.635668 
0.854516 
1.09827 
1.36476 
1.64982 
1.94708 
2.24791 
2.54162 
2.81605 
0.853632 
1.10165 
1.37791 
1.6799 
2.0029 
2.33964 
2.68036 
3.01299 
3.32384 
1.10101 
1.38203 
1.69505 
2.03719 
2.40307 
2.78444 
3.17017 
3.54659 
3.89841 
1.38175 
1.7001 
2.0547 
2.4423 
2.85672 
3.28857 
3.72511 
4.15065 
4.54784 
1.70048 
2.0609 
2.46256 
2.90164 
3.37108 
3.86017 
4.35432 
4.835 
5.27915 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
1.44727
0.979506
0.680661
0.45885
0.270449
0.0962563
-0.0719041
-0.237488
-0.401962
-0.565955
-0.729738
-0.893428
-1.05708
-1.22071
-1.38433
-1.54795
-1.71157
-1.87519
-2.0388
-2.20242
-2.36604
-2.52965
-2.69327
-2.85689
-3.0205
-3.18412
-3.34774
-3.51135
-3.67497
-3.83859
-4.0022
-4.16582
-4.32944
-4.49305
-4.65667
-4.82029
-4.9839
-5.14752
-5.31114
-5.47475
-5.63837
-5.80199
-5.9656
-6.12922
-6.29284
-6.45645
-6.62007
-6.78369
-6.9473
-7.11092
-7.27454
-7.43815
-7.60177
-7.76539
-7.929
-8.09262
-8.25624
-8.41985
-8.58347
-8.74709
-8.9107
-9.07432
-9.23794
-9.40155
-9.56517
-9.72878
-9.8924
-10.056
-10.2196
-10.3833
-10.5469
-10.7105
-10.8741
-11.0377
-11.2013
-11.365
-11.5286
-11.6922
-11.8558
-12.0194
-12.183
-12.3467
-12.5103
-12.6739
-12.8375
-13.0011
-13.1647
-13.3284
-13.492
-13.6556
-13.8192
-13.9828
-14.1464
-14.3101
-14.4737
-14.6373
-14.8009
-14.9645
-15.1281
-15.2918
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0 
0.0641227 
0.132325 
0.204407 
0.280191 
0.359456 
0.441916 
0.527203 
0.614868 
0.704375 
0.795099 
0.886333 
0.977288 
1.0671 
1.15483 
1.23949 
1.31993 
0.064109 
0.132633 
0.205301 
0.28205 
0.362725 
0.447101 
0.534874 
0.625656 
0.718967 
0.814237 
0.910804 
1.00791 
1.10473 
1.20033 
1.29374 
1.38392 
1.46986 
0.132552 
0.205561 
0.282961 
0.36468 
0.450568 
0.540388 
0.63382 
0.730452 
0.829775 
0.931184 
1.03397 
1.13734 
1.2404 
1.34217 
1.44162 
1.53767 
1.62923 
0.205477 
0.283213 
0.365627 
0.452632 
0.544067 
0.639683 
0.739141 
0.842002 
0.947728 
1.05567 
1.16509 
1.27512 
1.38482 
1.49317 
1.59905 
1.70132 
1.7988 
0.283133 
0.36589 
0.453629 
0.546254 
0.643592 
0.745377 
0.851249 
0.960743 
1.07328 
1.18819 
1.30466 
1.42178 
1.53856 
1.6539 
1.76662 
1.87549 
1.97927 
0.365813 
0.453909 
0.547312 
0.645916 
0.749535 
0.857886 
0.970586 
1.08714 
1.20694 
1.32925 
1.45322 
1.5779 
1.70221 
1.82499 
1.94498 
2.06089 
2.17136 
0.453835 
0.547614 
0.647042 
0.752008 
0.862311 
0.977651 
1.09762 
1.22169 
1.34921 
1.4794 
1.61137 
1.74409 
1.87641 
2.00711 
2.13484 
2.25822 
2.37581 
0.547541 
0.647369 
0.753211 
0.864947 
0.982363 
1.10514 
1.23284 
1.36491 
1.50065 
1.63924 
1.77971 
1.92098 
2.06184 
2.20096 
2.33693 
2.46827 
2.59344 
0.647298 
0.753564 
0.866232 
0.985173 
1.11016 
1.24085 
1.37679 
1.51737 
1.66186 
1.80938 
1.9589 
2.10928 
2.25922 
2.4073 
2.55204 
2.69184 
2.82509 
0.753495 
0.866614 
0.986547 
1.11316 
1.2462 
1.38532 
1.53002 
1.67966 
1.83346 
1.99049 
2.14965 
2.30972 
2.46931 
2.62694 
2.78101 
2.92982 
3.07166 
0.866549 
0.986963 
1.11463 
1.2494 
1.39103 
1.53911 
1.69313 
1.85242 
2.01613 
2.18327 
2.35269 
2.52307 
2.69295 
2.86073 
3.02472 
3.18313 
3.33411 
0.986902 
1.11508 
1.25098 
1.39444 
1.54519 
1.70283 
1.86677 
2.03632 
2.21058 
2.3885 
2.56883 
2.75018 
2.931 
3.10959 
3.28413 
3.45274 
3.61347 
1.11503 
1.25147 
1.39613 
1.54884 
1.70931 
1.8771 
2.05162 
2.23209 
2.41758 
2.60695 
2.7989 
2.99193 
3.18439 
3.37447 
3.56025 
3.73972 
3.9108 
1.25143 
1.39667 
1.55066 
1.71321 
1.88402 
2.06263 
2.24839 
2.44049 
2.63793 
2.8395 
3.04381 
3.24927 
3.45412 
3.65643 
3.85416 
4.04516 
4.22725 
1.39664 
1.55125 
1.71516 
1.88819 
2.07001 
2.26013 
2.45786 
2.66234 
2.8725 
3.08706 
3.30453 
3.52322 
3.74124 
3.95656 
4.16698 
4.37023 
4.56401 
1.55123 
1.71581 
1.89028 
2.07447 
2.26801 
2.47038 
2.68085 
2.89851 
3.12221 
3.35059 
3.58206 
3.81483 
4.04689 
4.27605 
4.49997 
4.7162 
4.92228 
1.71583 
1.891 
2.07672 
2.27277 
2.47879 
2.6942 
2.91823 
3.14992 
3.38803 
3.63113 
3.87751 
4.12528 
4.37228 
4.61619 
4.85448 
5.08446 
5.30308 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
1.71583
1.28426
0.981393
0.760085
0.5865
0.439503
0.306956
0.182182
0.0615788
-0.0567824
-0.173935
-0.290433
-0.406577
-0.522526
-0.63837
-0.754156
-0.869911
-0.985647
-1.10137
-1.2171
-1.33281
-1.44853
-1.56425
-1.67996
-1.79568
-1.91139
-2.02711
-2.14282
-2.25854
-2.37425
-2.48997
-2.60569
-2.7214
-2.83712
-2.95283
-3.06855
-3.18426
-3.29998
-3.41569
-3.53141
-3.64712
-3.76284
-3.87855
-3.99427
-4.10998
-4.2257
-4.34141
-4.45713
-4.57284
-4.68856
-4.80427
-4.91999
-5.0357
-5.15142
-5.26713
-5.38285
-5.49856
-5.61428
-5.72999
-5.84571
-5.96142
-6.07714
-6.19285
-6.30857
-6.42428
-6.54
-6.65571
-6.77143
-6.88714
-7.00286
-7.11857
-7.23429
-7.35
-7.46572
-7.58143
-7.69715
-7.81286
-7.92858
-8.04429
-8.16001
-8.27572
-8.39144
-8.50715
-8.62287
-8.73859
-8.8543
-8.97002
-9.08573
-9.20145
-9.31716
-9.43288
-9.54859
-9.66431
-9.78002
-9.89574
-10.0115
-10.1272
-10.2429
-10.3586
-10.4743
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0 
0.0301088 
0.0620957 
0.095364 
0.12973 
0.16512 
0.20149 
0.238808 
0.27704 
0.316154 
0.356113 
0.396878 
0.438403 
0.480639 
0.523532 
0.567023 
0.611048 
0.655535 
0.700409 
0.745591 
0.790994 
0.836527 
0.882094 
0.927595 
0.972924 
1.01797 
1.06263 
1.10677 
1.15029 
1.19306 
1.23495 
1.27583 
1.31557 
0.0301078 
0.0624118 
0.0957323 
0.130155 
0.165651 
0.202184 
0.23972 
0.27823 
0.317681 
0.358041 
0.399272 
0.441333 
0.484178 
0.527757 
0.572014 
0.616886 
0.662309 
0.708209 
0.754509 
0.801125 
0.847969 
0.894948 
0.941961 
0.988907 
1.03567 
1.08215 
1.12823 
1.17377 
1.21867 
1.26279 
1.30602 
1.34821 
1.38925 
0.0621244 
0.0957632 
0.130354 
0.165984 
0.202667 
0.240393 
0.279141 
0.318887 
0.359601 
0.401249 
0.443794 
0.487194 
0.531403 
0.576368 
0.622031 
0.66833 
0.715196 
0.762554 
0.810324 
0.858421 
0.906753 
0.955223 
1.00373 
1.05217 
1.10042 
1.14837 
1.19591 
1.2429 
1.28922 
1.33475 
1.37935 
1.42289 
1.46524 
0.09549 
0.130287 
0.166086 
0.20293 
0.240834 
0.279794 
0.319798 
0.360823 
0.402841 
0.44582 
0.489722 
0.534506 
0.580122 
0.626517 
0.673633 
0.721404 
0.769759 
0.818622 
0.86791 
0.917535 
0.967402 
1.01741 
1.06746 
1.11743 
1.16722 
1.21669 
1.26574 
1.31422 
1.36202 
1.40899 
1.45501 
1.49993 
1.54363 
0.130062 
0.165996 
0.202988 
0.241056 
0.280206 
0.320437 
0.361735 
0.40408 
0.447445 
0.491799 
0.537103 
0.583314 
0.630384 
0.678256 
0.72687 
0.77616 
0.826053 
0.876469 
0.927323 
0.978524 
1.02997 
1.08157 
1.13321 
1.18477 
1.23614 
1.28718 
1.33779 
1.38781 
1.43712 
1.48559 
1.53307 
1.57942 
1.62451 
0.165812 
0.2029 
0.241097 
0.280408 
0.320834 
0.362369 
0.404999 
0.448705 
0.493461 
0.539233 
0.585983 
0.633668 
0.682237 
0.731633 
0.781795 
0.832652 
0.884131 
0.936149 
0.988619 
1.04145 
1.09453 
1.14777 
1.20105 
1.25424 
1.30724 
1.35991 
1.41212 
1.46373 
1.51461 
1.56462 
1.61361 
1.66143 
1.70795 
0.202746 
0.241019 
0.280446 
0.321028 
0.36276 
0.405635 
0.449636 
0.494745 
0.540934 
0.588169 
0.636412 
0.685618 
0.735734 
0.786703 
0.83846 
0.890936 
0.944051 
0.997723 
1.05186 
1.10637 
1.16114 
1.21607 
1.27104 
1.32592 
1.3806 
1.43495 
1.48881 
1.54207 
1.59456 
1.64616 
1.6967 
1.74604 
1.79404 
0.240888 
0.28038 
0.32107 
0.362955 
0.406028 
0.45028 
0.495693 
0.542247 
0.589913 
0.638657 
0.68844 
0.739214 
0.790927 
0.843518 
0.896923 
0.951067 
1.00587 
1.06125 
1.11711 
1.17335 
1.22986 
1.28653 
1.34325 
1.39988 
1.45629 
1.51236 
1.56794 
1.62288 
1.67705 
1.73028 
1.78243 
1.83334 
1.88286 
0.280267 
0.321014 
0.363003 
0.406228 
0.450681 
0.49635 
0.543217 
0.591259 
0.640448 
0.690748 
0.742118 
0.79451 
0.84787 
0.902136 
0.95724 
1.01311 
1.06965 
1.12679 
1.18443 
1.24245 
1.30076 
1.35923 
1.41775 
1.47618 
1.53439 
1.59223 
1.64958 
1.70627 
1.76215 
1.81707 
1.87088 
1.9234 
1.97449 
0.320915 
0.362958 
0.406284 
0.450888 
0.496761 
0.543889 
0.592254 
0.64183 
0.692589 
0.744493 
0.797501 
0.851562 
0.906621 
0.962614 
1.01947 
1.07711 
1.13546 
1.19441 
1.25388 
1.31375 
1.37391 
1.43424 
1.49461 
1.5549 
1.61496 
1.67464 
1.73381 
1.7923 
1.84995 
1.90662 
1.96213 
2.01633 
2.06904 
0.362869 
0.406248 
0.450953 
0.496978 
0.544314 
0.592945 
0.642853 
0.694011 
0.746388 
0.799946 
0.854642 
0.910425 
0.967236 
1.02501 
1.08368 
1.14315 
1.20335 
1.26418 
1.32554 
1.38731 
1.44938 
1.51163 
1.57392 
1.63612 
1.69808 
1.75967 
1.82071 
1.88106 
1.94054 
1.99901 
2.05628 
2.1122 
2.16658 
0.406168 
0.450924 
0.497051 
0.544542 
0.593385 
0.643566 
0.695064 
0.747851 
0.801897 
0.857162 
0.913599 
0.971157 
1.02978 
1.08939 
1.14992 
1.21129 
1.2734 
1.33616 
1.39947 
1.4632 
1.52724 
1.59147 
1.65574 
1.71992 
1.78385 
1.84739 
1.91037 
1.97263 
2.03401 
2.09433 
2.15342 
2.21111 
2.26722 
0.450853 
0.49703 
0.544623 
0.593624 
0.644021 
0.6958 
0.748937 
0.803406 
0.859172 
0.916196 
0.974429 
1.03382 
1.0943 
1.15581 
1.21827 
1.28158 
1.34567 
1.41043 
1.47574 
1.5415 
1.60758 
1.67385 
1.74016 
1.80637 
1.87234 
1.93789 
2.00287 
2.06711 
2.13044 
2.19268 
2.25365 
2.31317 
2.37106 
0.496964 
0.544608 
0.593713 
0.644272 
0.696272 
0.749698 
0.804526 
0.860728 
0.918268 
0.977106 
1.03719 
1.09847 
1.16088 
1.22434 
1.28878 
1.35411 
1.42024 
1.48705 
1.55444 
1.62229 
1.69047 
1.75884 
1.82726 
1.89557 
1.96363 
2.03127 
2.09831 
2.16459 
2.22993 
2.29414 
2.35705 
2.41846 
2.47819 
0.544548 
0.593704 
0.644369 
0.696534 
0.750188 
0.805313 
0.861884 
0.919874 
0.979244 
1.03995 
1.10195 
1.16518 
1.22957 
1.29505 
1.36154 
1.42895 
1.49717 
1.56611 
1.63564 
1.70564 
1.77599 
1.84653 
1.91712 
1.98761 
2.05783 
2.12761 
2.19678 
2.26517 
2.33258 
2.39883 
2.46373 
2.52709 
2.58872 
0.593649 
0.644366 
0.69664 
0.750463 
0.805821 
0.862698 
0.921068 
0.980901 
1.04216 
1.1048 
1.16877 
1.234 
1.30044 
1.368 
1.43661 
1.50615 
1.57655 
1.64767 
1.71942 
1.79164 
1.86422 
1.937 
2.00983 
2.08256 
2.15501 
2.22701 
2.29838 
2.36893 
2.43849 
2.50684 
2.5738 
2.63917 
2.70276 
0.644315 
0.696642 
0.750576 
0.806108 
0.863226 
0.92191 
0.982135 
1.04387 
1.10707 
1.1717 
1.23771 
1.30502 
1.37356 
1.44327 
1.51406 
1.58581 
1.65844 
1.73183 
1.80585 
1.88037 
1.95525 
2.03035 
2.10549 
2.18053 
2.25528 
2.32956 
2.4032 
2.47599 
2.54775 
2.61828 
2.68737 
2.75481 
2.82041 
0.696595 
0.750583 
0.806229 
0.863525 
0.922457 
0.983005 
1.04514 
1.10884 
1.17405 
1.24074 
1.30884 
1.37828 
1.44901 
1.52094 
1.59397 
1.668 
1.74294 
1.81866 
1.89503 
1.97192 
2.04918 
2.12665 
2.20419 
2.2816 
2.35873 
2.43537 
2.51134 
2.58645 
2.66049 
2.73325 
2.80453 
2.87412 
2.94181 
0.750539 
0.806241 
0.863655 
0.92277 
0.983574 
1.04604 
1.11016 
1.17588 
1.24316 
1.31196 
1.38223 
1.45388 
1.52686 
1.60106 
1.67641 
1.7528 
1.83012 
1.90824 
1.98704 
2.06637 
2.14608 
2.22602 
2.30601 
2.38589 
2.46546 
2.54454 
2.62292 
2.70041 
2.7768 
2.85188 
2.92542 
2.99722 
3.06705 
0.806201 
0.863671 
0.922907 
0.9839 
1.04663 
1.11109 
1.17724 
1.24505 
1.31447 
1.38546 
1.45795 
1.53188 
1.60717 
1.68374 
1.76148 
1.8403 
1.92007 
2.00067 
2.08197 
2.16382 
2.24606 
2.32854 
2.41107 
2.49348 
2.57558 
2.65717 
2.73804 
2.81799 
2.89681 
2.97426 
3.05014 
3.12422 
3.19627 
0.863633 
0.922928 
0.984045 
1.04697 
1.1117 
1.1782 
1.24645 
1.31641 
1.38804 
1.46128 
1.53608 
1.61236 
1.69004 
1.76904 
1.84925 
1.93057 
2.01287 
2.09604 
2.17992 
2.26436 
2.34922 
2.43431 
2.51947 
2.60449 
2.6892 
2.77338 
2.85682 
2.93931 
3.02062 
3.10054 
3.17882 
3.25525 
3.32959 
0.922893 
0.984071 
1.04713 
1.11205 
1.17884 
1.24745 
1.31787 
1.39005 
1.46395 
1.53952 
1.61669 
1.69539 
1.77554 
1.85705 
1.93981 
2.02371 
2.10863 
2.19443 
2.28097 
2.3681 
2.45565 
2.54345 
2.6313 
2.71903 
2.80642 
2.89327 
2.97936 
3.06447 
3.14837 
3.23082 
3.31159 
3.39044 
3.46714 
0.984038 
1.04716 
1.11222 
1.1792 
1.24811 
1.3189 
1.39155 
1.46602 
1.54227 
1.62024 
1.69986 
1.78106 
1.86376 
1.94785 
2.03324 
2.1198 
2.20742 
2.29595 
2.38524 
2.47513 
2.56546 
2.65604 
2.74669 
2.8372 
2.92737 
3.01697 
3.1058 
3.19361 
3.28016 
3.36523 
3.44857 
3.52993 
3.60906 
1.04713 
1.11225 
1.17937 
1.24849 
1.31958 
1.39262 
1.46758 
1.54442 
1.62309 
1.70353 
1.78568 
1.86946 
1.95478 
2.04154 
2.12964 
2.21895 
2.30935 
2.40069 
2.49281 
2.58556 
2.67876 
2.77222 
2.86574 
2.95912 
3.05215 
3.1446 
3.23624 
3.32684 
3.41615 
3.50392 
3.5899 
3.67383 
3.75548 
1.11222 
1.17941 
1.24867 
1.31998 
1.39332 
1.46868 
1.54602 
1.6253 
1.70647 
1.78946 
1.87422 
1.96066 
2.04869 
2.13821 
2.2291 
2.32125 
2.41452 
2.50875 
2.6038 
2.6995 
2.79565 
2.89208 
2.98857 
3.08492 
3.1809 
3.27628 
3.37083 
3.4643 
3.55644 
3.647 
3.73571 
3.82231 
3.90654 
1.17939 
1.24871 
1.32016 
1.39374 
1.46941 
1.54716 
1.62696 
1.70875 
1.7925 
1.87813 
1.96558 
2.05476 
2.14558 
2.23794 
2.33172 
2.4268 
2.52302 
2.62025 
2.71832 
2.81705 
2.91626 
3.01574 
3.1153 
3.2147 
3.31373 
3.41214 
3.50969 
3.60613 
3.70119 
3.79462 
3.88615 
3.9755 
4.06241 
1.24869 
1.32021 
1.39393 
1.46984 
1.54792 
1.62814 
1.71046 
1.79486 
1.88126 
1.96961 
2.05983 
2.15185 
2.24555 
2.34085 
2.4376 
2.5357 
2.63498 
2.73529 
2.83647 
2.93834 
3.04069 
3.14333 
3.24605 
3.34861 
3.45078 
3.55231 
3.65296 
3.75246 
3.85054 
3.94693 
4.04136 
4.13355 
4.22321 
1.32019 
1.39399 
1.47005 
1.54837 
1.62892 
1.71169 
1.79663 
1.8837 
1.97284 
2.064 
2.15709 
2.25202 
2.3487 
2.44702 
2.54685 
2.64805 
2.75049 
2.85399 
2.95838 
3.06347 
3.16908 
3.27498 
3.38095 
3.48677 
3.59218 
3.69694 
3.80078 
3.90343 
4.00462 
4.10407 
4.2015 
4.29661 
4.38912 
1.39397 
1.47011 
1.54858 
1.62939 
1.7125 
1.79789 
1.88553 
1.97536 
2.06734 
2.16138 
2.25743 
2.35538 
2.45513 
2.55656 
2.65956 
2.76398 
2.86966 
2.97645 
3.08415 
3.19259 
3.30154 
3.4108 
3.52014 
3.62931 
3.73807 
3.84615 
3.95329 
4.0592 
4.1636 
4.2662 
4.36672 
4.46485 
4.56029 
1.47009 
1.54865 
1.62961 
1.71298 
1.79873 
1.88683 
1.97725 
2.06994 
2.16483 
2.26187 
2.36096 
2.46201 
2.56493 
2.66959 
2.77586 
2.88359 
2.99263 
3.1028 
3.21392 
3.3258 
3.43821 
3.55094 
3.66375 
3.77638 
3.88859 
4.0001 
4.11064 
4.21991 
4.32762 
4.43348 
4.53718 
4.63842 
4.73689 
1.54864 
1.62968 
1.71322 
1.79923 
1.8877 
1.9786 
2.07189 
2.16752 
2.26543 
2.36554 
2.46778 
2.57204 
2.67822 
2.7862 
2.89584 
3.00699 
3.11949 
3.23316 
3.34781 
3.46324 
3.57922 
3.69553 
3.81191 
3.92813 
4.04389 
4.15894 
4.27298 
4.38572 
4.49685 
4.60606 
4.71305 
4.81749 
4.91909 
1.62968 
1.7133 
1.79948 
1.88823 
1.97951 
2.07329 
2.16954 
2.2682 
2.36922 
2.47251 
2.57799 
2.68556 
2.79512 
2.90652 
3.01964 
3.13432 
3.25039 
3.36767 
3.48596 
3.60505 
3.72471 
3.8447 
3.96479 
4.08469 
4.20413 
4.32283 
4.44049 
4.5568 
4.67145 
4.78413 
4.8945 
5.00224 
5.10704 
1.71329 
1.79957 
1.88849 
1.98005 
2.07423 
2.17099 
2.27029 
2.37208 
2.4763 
2.58287 
2.6917 
2.80269 
2.91572 
3.03066 
3.14737 
3.26569 
3.38545 
3.50645 
3.62849 
3.75136 
3.87482 
3.99862 
4.12251 
4.24622 
4.36945 
4.49192 
4.61331 
4.73331 
4.8516 
4.96785 
5.08172 
5.19286 
5.30089 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
1.9257
1.55058
1.25609
1.02927
0.851777
0.707551
0.584799
0.475571
0.374753
0.279135
0.186726
0.0963007
0.00710241
-0.0813343
-0.169297
-0.256965
-0.344447
-0.431814
-0.519109
-0.606357
-0.693577
-0.780779
-0.867969
-0.955152
-1.04233
-1.12951
-1.21668
-1.30385
-1.39102
-1.47819
-1.56537
-1.65254
-1.73971
-1.82688
-1.91405
-2.00122
-2.08839
-2.17556
-2.26273
-2.3499
-2.43707
-2.52424
-2.61141
-2.69858
-2.78575
-2.87292
-2.96009
-3.04726
-3.13443
-3.2216
-3.30877
-3.39594
-3.48312
-3.57029
-3.65746
-3.74463
-3.8318
-3.91897
-4.00614
-4.09331
-4.18048
-4.26765
-4.35482
-4.44199
-4.52916
-4.61633
-4.7035
-4.79067
-4.87784
-4.96501
-5.05218
-5.13935
-5.22652
-5.31369
-5.40086
-5.48803
-5.57521
-5.66238
-5.74955
-5.83672
-5.92389
-6.01106
-6.09823
-6.1854
-6.27257
-6.35974
-6.44691
-6.53408
-6.62125
-6.70842
-6.79559
-6.88276
-6.96993
-7.0571
-7.14427
-7.23144
-7.31861
-7.40578
-7.49295
-7.58012
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd2.png');
clf
figure(2);
saveas(gcf,'oneResidualInd2.png');

N = [
4
8
16
32
];
E = [
-2.34313
-5.22931
-8.51592
-7.64703
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2e-05
0.000331
0.006063
0.354826
];
T2 = [
0.010302
0.081921
1.01508
14.4966
];
figure(4);
subplot(3,1,2);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
1.00064 
1.27905 
1.61427 
1.97808 
2.31978 
1.27851 
1.63851 
2.06891 
2.53616 
2.97865 
1.63891 
2.1014 
2.654 
3.25447 
3.82467 
2.10476 
2.6974 
3.40603 
4.17697 
4.91097 
2.70846 
3.46403 
4.37158 
5.35976 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.183161
-1.19478
-2.19645
-3.2702
-4.36093
-5.4557
-6.55142
-7.64738
-8.74339
-9.83942
-10.9355
-12.0315
-13.1275
-14.2235
-15.3196
-16.4156
-17.5116
-18.6077
-19.7037
-20.7997
-21.8958
-22.9918
-24.0878
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0.998476 
1.13115 
1.27919 
1.44111 
1.61429 
1.79476 
1.97714 
2.15474 
2.31978 
1.13107 
1.28153 
1.44926 
1.63267 
1.82883 
2.03324 
2.23985 
2.44117 
2.62865 
1.28143 
1.45195 
1.64199 
1.84979 
2.07202 
2.30361 
2.53774 
2.76597 
2.97865 
1.45188 
1.6451 
1.86044 
2.09587 
2.34766 
2.61008 
2.87541 
3.13411 
3.37526 
1.6451 
1.86404 
2.10803 
2.37478 
2.66006 
2.95741 
3.2581 
3.5513 
3.82467 
1.86414 
2.11222 
2.38865 
2.69087 
3.01409 
3.35101 
3.69174 
4.02405 
4.33391 
2.11246 
2.39354 
2.70671 
3.0491 
3.41528 
3.797 
4.18308 
4.55969 
4.91097 
2.39404 
2.71244 
3.06721 
3.45508 
3.8699 
4.30232 
4.73972 
5.16652 
5.56486 
2.71348 
3.07396 
3.47581 
3.91518 
4.38505 
4.87483 
5.37024 
5.85375 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.41333
-0.978451
-1.75424
-2.56425
-3.40475
-4.26068
-5.12436
-5.99192
-6.86141
-7.73185
-8.60278
-9.47394
-10.3452
-11.2166
-12.0879
-12.9593
-13.8307
-14.7021
-15.5735
-16.4449
-17.3163
-18.1877
-19.0591
-19.9305
-20.8019
-21.6733
-22.5448
-23.4162
-24.2876
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0.999512 
1.06396 
1.1323 
1.20444 
1.28026 
1.35954 
1.44199 
1.52726 
1.6149 
1.70437 
1.79504 
1.88622 
1.97711 
2.06686 
2.15454 
2.23919 
2.31978 
1.06395 
1.13256 
1.2053 
1.2821 
1.3628 
1.44719 
1.53496 
1.62572 
1.719 
1.81423 
1.91075 
2.0078 
2.10455 
2.20008 
2.29342 
2.38354 
2.46939 
1.13255 
1.20559 
1.28302 
1.36477 
1.45067 
1.5405 
1.63392 
1.73053 
1.82982 
1.93119 
2.03393 
2.13724 
2.24022 
2.34192 
2.44128 
2.53723 
2.62865 
1.20557 
1.28332 
1.36575 
1.45277 
1.54421 
1.63982 
1.73927 
1.84211 
1.9478 
2.0557 
2.16506 
2.27503 
2.38466 
2.49292 
2.5987 
2.70085 
2.79818 
1.28331 
1.36607 
1.45381 
1.54644 
1.64378 
1.74556 
1.85141 
1.96088 
2.07339 
2.18824 
2.30466 
2.42172 
2.53842 
2.65366 
2.76628 
2.87503 
2.97865 
1.36606 
1.45416 
1.54756 
1.64616 
1.74978 
1.85811 
1.97079 
2.08732 
2.20708 
2.32934 
2.45326 
2.57787 
2.7021 
2.82479 
2.94467 
3.06044 
3.17076 
1.45415 
1.54793 
1.64736 
1.75232 
1.86261 
1.97793 
2.09788 
2.22192 
2.3494 
2.47955 
2.61146 
2.74411 
2.87635 
3.00695 
3.13457 
3.25781 
3.37526 
1.54793 
1.64775 
1.75359 
1.86532 
1.98272 
2.10548 
2.23316 
2.3652 
2.5009 
2.63944 
2.77986 
2.92106 
3.06184 
3.20086 
3.33672 
3.46792 
3.59294 
1.64775 
1.75402 
1.86668 
1.98561 
2.11059 
2.24126 
2.37717 
2.51772 
2.66217 
2.80965 
2.95912 
3.10943 
3.25929 
3.40728 
3.5519 
3.69157 
3.82467 
1.75402 
1.86714 
1.98707 
2.11367 
2.2467 
2.3858 
2.53048 
2.68009 
2.83385 
2.99084 
3.14995 
3.30996 
3.46948 
3.62702 
3.78097 
3.92965 
4.07134 
1.86715 
1.98756 
2.11523 
2.24999 
2.3916 
2.53967 
2.69367 
2.85293 
3.01661 
3.18371 
3.35308 
3.52341 
3.69322 
3.86092 
4.02481 
4.18309 
4.33391 
1.98758 
2.11576 
2.25165 
2.39511 
2.54585 
2.70346 
2.86739 
3.03691 
3.21115 
3.38902 
3.56932 
3.75063 
3.93139 
4.10991 
4.28437 
4.45287 
4.61343 
2.11579 
2.25223 
2.39689 
2.54959 
2.71005 
2.87782 
3.05232 
3.23277 
3.41823 
3.60758 
3.7995 
3.9925 
4.18492 
4.37495 
4.56067 
4.74004 
4.91097 
2.25227 
2.39751 
2.55149 
2.71404 
2.88484 
3.06343 
3.24917 
3.44126 
3.63868 
3.84023 
4.04452 
4.24996 
4.45479 
4.65708 
4.85478 
5.04573 
5.2277 
2.39756 
2.55217 
2.71608 
2.8891 
3.07092 
3.26102 
3.45873 
3.6632 
3.87334 
4.08788 
4.30534 
4.52402 
4.74205 
4.95738 
5.16784 
5.37112 
5.56486 
2.55224 
2.71682 
2.89129 
3.07547 
3.269 
3.47135 
3.68181 
3.89945 
4.12314 
4.3515 
4.58297 
4.81574 
5.04782 
5.27704 
5.50107 
5.71747 
5.92376 
2.71692 
2.89209 
3.07781 
3.27386 
3.47986 
3.69526 
3.91928 
4.15095 
4.38905 
4.63213 
4.87851 
5.12627 
5.3733 
5.61728 
5.85574 
6.08611 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.793794
-0.507551
-1.56952
-2.30172
-2.96098
-3.64039
-4.33309
-5.0345
-5.74162
-6.45247
-7.16576
-7.88064
-8.59656
-9.31315
-10.0302
-10.7475
-11.465
-12.1827
-12.9004
-13.6182
-14.336
-15.0538
-15.7717
-16.4895
-17.2074
-17.9252
-18.6431
-19.361
-20.0789
-20.7967
-21.5146
-22.2325
-22.9503
-23.6682
-24.3861
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0.999871 
1.03161 
1.06432 
1.09801 
1.13265 
1.16825 
1.20479 
1.24224 
1.28058 
1.31979 
1.35983 
1.40067 
1.44226 
1.48455 
1.52749 
1.57102 
1.61508 
1.6596 
1.7045 
1.74971 
1.79513 
1.84068 
1.88626 
1.93178 
1.97711 
2.02217 
2.06683 
2.11097 
2.15449 
2.19725 
2.23914 
2.28002 
2.31978 
1.03161 
1.06435 
1.09811 
1.13286 
1.16861 
1.20534 
1.24303 
1.28167 
1.32123 
1.36168 
1.403 
1.44513 
1.48803 
1.53167 
1.57597 
1.62089 
1.66634 
1.71228 
1.7586 
1.80524 
1.85211 
1.8991 
1.94613 
1.99309 
2.03986 
2.08635 
2.13242 
2.17797 
2.22287 
2.26699 
2.3102 
2.35239 
2.39341 
1.06435 
1.09814 
1.13296 
1.16882 
1.2057 
1.24359 
1.28249 
1.32235 
1.36317 
1.40491 
1.44753 
1.491 
1.53527 
1.58028 
1.62599 
1.67233 
1.71923 
1.76662 
1.81442 
1.86254 
1.91089 
1.95938 
2.0079 
2.05635 
2.10461 
2.15257 
2.20011 
2.2471 
2.29342 
2.33894 
2.38353 
2.42706 
2.46939 
1.09814 
1.133 
1.16892 
1.20592 
1.24397 
1.28307 
1.32319 
1.36432 
1.40644 
1.4495 
1.49347 
1.53832 
1.584 
1.63044 
1.6776 
1.72541 
1.7738 
1.8227 
1.87201 
1.92166 
1.97155 
2.02157 
2.07163 
2.12162 
2.17141 
2.22089 
2.26994 
2.31842 
2.36621 
2.41318 
2.45919 
2.5041 
2.54778 
1.13299 
1.16896 
1.20603 
1.2442 
1.28346 
1.3238 
1.36519 
1.40763 
1.45108 
1.49551 
1.54088 
1.58715 
1.63427 
1.68219 
1.73085 
1.78018 
1.8301 
1.88055 
1.93143 
1.98265 
2.03412 
2.08574 
2.13739 
2.18896 
2.24033 
2.29138 
2.34199 
2.39201 
2.44132 
2.48978 
2.53725 
2.58358 
2.62865 
1.16896 
1.20606 
1.24431 
1.28369 
1.3242 
1.36581 
1.40853 
1.45231 
1.49714 
1.54298 
1.58979 
1.63753 
1.68615 
1.73559 
1.78579 
1.83668 
1.88819 
1.94024 
1.99273 
2.04558 
2.09869 
2.15194 
2.20523 
2.25843 
2.31144 
2.36411 
2.41632 
2.46793 
2.51881 
2.56881 
2.61778 
2.66559 
2.71209 
1.20606 
1.24435 
1.28381 
1.32444 
1.36623 
1.40917 
1.45324 
1.49841 
1.54466 
1.59195 
1.64025 
1.68951 
1.73967 
1.79068 
1.84247 
1.89498 
1.94813 
2.00182 
2.05599 
2.11051 
2.1653 
2.22024 
2.27522 
2.33012 
2.38481 
2.43915 
2.49302 
2.54627 
2.59876 
2.65035 
2.70088 
2.75021 
2.79818 
1.24434 
1.28384 
1.32456 
1.36648 
1.4096 
1.4539 
1.49936 
1.54597 
1.59369 
1.64249 
1.69231 
1.74313 
1.79489 
1.84752 
1.90095 
1.95513 
2.00996 
2.06536 
2.12124 
2.1775 
2.23403 
2.29072 
2.34744 
2.40408 
2.4605 
2.51657 
2.57215 
2.62709 
2.68125 
2.73448 
2.78661 
2.83751 
2.88701 
1.28384 
1.3246 
1.3666 
1.40985 
1.45434 
1.50005 
1.54696 
1.59504 
1.64428 
1.69462 
1.74603 
1.79846 
1.85186 
1.90616 
1.96129 
2.01719 
2.07376 
2.13092 
2.18858 
2.24662 
2.30494 
2.36343 
2.42195 
2.48039 
2.5386 
2.59645 
2.6538 
2.71048 
2.76636 
2.82128 
2.87507 
2.92758 
2.97865 
1.32459 
1.36664 
1.40998 
1.4546 
1.5005 
1.54766 
1.59606 
1.64567 
1.69647 
1.74841 
1.80145 
1.85555 
1.91064 
1.96666 
2.02355 
2.08122 
2.13959 
2.19856 
2.25805 
2.31793 
2.3781 
2.43845 
2.49883 
2.55912 
2.61918 
2.67887 
2.73803 
2.79652 
2.85417 
2.91083 
2.96633 
3.02051 
3.0732 
1.36664 
1.41002 
1.45474 
1.50078 
1.54813 
1.59679 
1.64672 
1.69791 
1.75032 
1.80391 
1.85864 
1.91445 
1.97129 
2.02909 
2.08778 
2.14728 
2.2075 
2.26835 
2.32972 
2.39151 
2.45359 
2.51585 
2.57815 
2.64035 
2.70232 
2.7639 
2.82495 
2.88529 
2.94477 
3.00323 
3.06049 
3.11639 
3.17076 
1.41002 
1.45478 
1.50091 
1.54841 
1.59727 
1.64747 
1.69899 
1.75181 
1.80588 
1.86117 
1.91763 
1.97522 
2.03386 
2.0935 
2.15405 
2.21544 
2.27757 
2.34035 
2.40367 
2.46742 
2.53147 
2.59571 
2.65998 
2.72416 
2.7881 
2.85164 
2.91462 
2.97688 
3.03825 
3.09856 
3.15764 
3.21532 
3.27141 
1.45478 
1.50096 
1.54855 
1.59756 
1.64797 
1.69977 
1.75292 
1.80741 
1.8632 
1.92025 
1.9785 
2.03792 
2.09842 
2.15995 
2.22242 
2.28576 
2.34987 
2.41464 
2.47997 
2.54574 
2.61183 
2.6781 
2.74442 
2.81064 
2.8766 
2.94216 
3.00713 
3.07137 
3.13469 
3.19692 
3.25787 
3.31738 
3.37526 
1.50096 
1.5486 
1.59771 
1.64828 
1.70029 
1.75372 
1.80857 
1.86479 
1.92234 
1.9812 
2.04131 
2.1026 
2.16503 
2.22851 
2.29297 
2.35832 
2.42446 
2.49128 
2.55869 
2.62655 
2.69473 
2.76311 
2.83153 
2.89985 
2.96791 
3.03555 
3.10259 
3.16886 
3.23419 
3.2984 
3.36129 
3.42268 
3.4824 
1.5486 
1.59776 
1.64843 
1.7006 
1.75426 
1.80939 
1.86598 
1.92398 
1.98336 
2.04409 
2.1061 
2.16935 
2.23375 
2.29925 
2.36575 
2.43317 
2.50141 
2.57036 
2.63991 
2.70992 
2.78027 
2.85082 
2.92141 
2.9919 
3.06212 
3.1319 
3.20107 
3.26945 
3.33686 
3.4031 
3.46799 
3.53133 
3.59294 
1.59776 
1.64848 
1.70075 
1.75458 
1.80994 
1.86683 
1.92521 
1.98505 
2.04632 
2.10897 
2.17296 
2.23821 
2.30466 
2.37223 
2.44085 
2.51041 
2.58081 
2.65195 
2.7237 
2.79594 
2.86852 
2.94131 
3.01414 
3.08687 
3.15932 
3.23132 
3.30268 
3.37323 
3.44278 
3.51112 
3.57807 
3.64343 
3.70699 
1.64848 
1.7008 
1.75474 
1.81027 
1.8674 
1.92609 
1.98632 
2.04806 
2.11128 
2.17592 
2.24193 
2.30925 
2.37781 
2.44753 
2.51833 
2.5901 
2.66274 
2.73613 
2.81016 
2.88469 
2.95958 
3.03467 
3.10982 
3.18486 
3.25961 
3.33389 
3.40752 
3.48031 
3.55206 
3.62258 
3.69165 
3.75908 
3.82467 
1.7008 
1.75479 
1.81044 
1.86774 
1.92667 
1.98723 
2.04937 
2.11307 
2.1783 
2.24499 
2.3131 
2.38255 
2.45329 
2.52523 
2.59827 
2.67231 
2.74726 
2.82298 
2.89936 
2.97626 
3.05352 
3.131 
3.20853 
3.28595 
3.36307 
3.43972 
3.51569 
3.59079 
3.66482 
3.73757 
3.80884 
3.87841 
3.94607 
1.75479 
1.8105 
1.86791 
1.92703 
1.98783 
2.05031 
2.11442 
2.18015 
2.24744 
2.31625 
2.38652 
2.45818 
2.53117 
2.60538 
2.68074 
2.75714 
2.83446 
2.91259 
2.99139 
3.07073 
3.15045 
3.23039 
3.31038 
3.39026 
3.46983 
3.5489 
3.62728 
3.70477 
3.78115 
3.85621 
3.92974 
4.00152 
4.07134 
1.8105 
1.86797 
1.9272 
1.9882 
2.05093 
2.11539 
2.18154 
2.24935 
2.31878 
2.38978 
2.46228 
2.53621 
2.61151 
2.68809 
2.76584 
2.84466 
2.92444 
3.00505 
3.08635 
3.1682 
3.25045 
3.33293 
3.41546 
3.49787 
3.57997 
3.66155 
3.74242 
3.82237 
3.90117 
3.97862 
4.05448 
4.12854 
4.20057 
1.86797 
1.92726 
1.98838 
2.05131 
2.11604 
2.18254 
2.25079 
2.32076 
2.39239 
2.46564 
2.54044 
2.61672 
2.69441 
2.77341 
2.85363 
2.93496 
3.01727 
3.10043 
3.18432 
3.26877 
3.35363 
3.43872 
3.52388 
3.6089 
3.69361 
3.77778 
3.86122 
3.9437 
4.02501 
4.10491 
4.18319 
4.2596 
4.33391 
1.92727 
1.98844 
2.0515 
2.11643 
2.18321 
2.25182 
2.32224 
2.39443 
2.46833 
2.5439 
2.62108 
2.69978 
2.77994 
2.86145 
2.94421 
3.02812 
3.11304 
3.19885 
3.2854 
3.37253 
3.46008 
3.54788 
3.63574 
3.72346 
3.81085 
3.8977 
3.98378 
4.06889 
4.15277 
4.23522 
4.31597 
4.39481 
4.47149 
1.98844 
2.05156 
2.11662 
2.18361 
2.25251 
2.3233 
2.39596 
2.47043 
2.54668 
2.62466 
2.70428 
2.78548 
2.86818 
2.95228 
3.03767 
3.12424 
3.21186 
3.30039 
3.38969 
3.47958 
3.56991 
3.6605 
3.75114 
3.84165 
3.93182 
4.02142 
4.11024 
4.19804 
4.2846 
4.36965 
4.45298 
4.53432 
4.61343 
2.05157 
2.11669 
2.18381 
2.25293 
2.32401 
2.39705 
2.47201 
2.54885 
2.62753 
2.70797 
2.79012 
2.87391 
2.95923 
3.046 
3.1341 
3.22341 
3.31381 
3.40516 
3.49728 
3.59003 
3.68323 
3.77669 
3.87021 
3.9636 
4.05663 
4.14907 
4.24071 
4.3313 
4.4206 
4.50836 
4.59433 
4.67825 
4.75987 
2.11669 
2.18388 
2.25314 
2.32444 
2.39779 
2.47315 
2.55049 
2.62977 
2.71093 
2.79393 
2.87869 
2.96513 
3.05316 
3.14269 
3.23358 
3.32574 
3.419 
3.51324 
3.6083 
3.70399 
3.80015 
3.89657 
3.99306 
4.08941 
4.18539 
4.28078 
4.37532 
4.46879 
4.56092 
4.65147 
4.74017 
4.82675 
4.91097 
2.18389 
2.25321 
2.32466 
2.39823 
2.47391 
2.55166 
2.63145 
2.71324 
2.79699 
2.88262 
2.97007 
3.05926 
3.15008 
3.24245 
3.33623 
3.4313 
3.52753 
3.62476 
3.72283 
3.82157 
3.92077 
4.02026 
4.11981 
4.21922 
4.31825 
4.41666 
4.51421 
4.61064 
4.7057 
4.79912 
4.89063 
4.97997 
5.06686 
2.25321 
2.32474 
2.39846 
2.47436 
2.55244 
2.63266 
2.71498 
2.79937 
2.88578 
2.97413 
3.06435 
3.15637 
3.25008 
3.34537 
3.44213 
3.54022 
3.63951 
3.73983 
3.84101 
3.94287 
4.04523 
4.14787 
4.25059 
4.35315 
4.45532 
4.55685 
4.6575 
4.75699 
4.85507 
4.95146 
5.04588 
5.13805 
5.2277 
2.32474 
2.39854 
2.4746 
2.55291 
2.63346 
2.71623 
2.80117 
2.88824 
2.97738 
3.06854 
3.16163 
3.25656 
3.35325 
3.45157 
3.5514 
3.6526 
3.75504 
3.85854 
3.96293 
4.06803 
4.17363 
4.27954 
4.38551 
4.49133 
4.59674 
4.7015 
4.80534 
4.90799 
5.00918 
5.10863 
5.20605 
5.30115 
5.39364 
2.39854 
2.47468 
2.55315 
2.63395 
2.71706 
2.80245 
2.89009 
2.97992 
3.0719 
3.16595 
3.26199 
3.35994 
3.45969 
3.56113 
3.66413 
3.76855 
3.87423 
3.98102 
4.08873 
4.19716 
4.30612 
4.41538 
4.52472 
4.63389 
4.74265 
4.85073 
4.95787 
5.06378 
5.16818 
5.27079 
5.3713 
5.46942 
5.56486 
2.47468 
2.55324 
2.6342 
2.71757 
2.80332 
2.89142 
2.98184 
3.07452 
3.16941 
3.26645 
3.36554 
3.4666 
3.56951 
3.67417 
3.78044 
3.88817 
3.99721 
4.10739 
4.21851 
4.33039 
4.4428 
4.55553 
4.66834 
4.78098 
4.89319 
5.0047 
5.11524 
5.22451 
5.33223 
5.43809 
5.5418 
5.64304 
5.7415 
2.55325 
2.63429 
2.71783 
2.80384 
2.89231 
2.98321 
3.07649 
3.17212 
3.27003 
3.37014 
3.47238 
3.57664 
3.68282 
3.7908 
3.90045 
4.0116 
4.1241 
4.23777 
4.35242 
4.46785 
4.58383 
4.70014 
4.81652 
4.93274 
5.04851 
5.16356 
5.27761 
5.39035 
5.50148 
5.61071 
5.7177 
5.82216 
5.92376 
2.6343 
2.71792 
2.80411 
2.89285 
2.98413 
3.07791 
3.17416 
3.27282 
3.37383 
3.47712 
3.5826 
3.69018 
3.79973 
3.91114 
4.02426 
4.13894 
4.25501 
4.37229 
4.49058 
4.60967 
4.72933 
4.84933 
4.96941 
5.08931 
5.20876 
5.32746 
5.44512 
5.56144 
5.67611 
5.7888 
5.89919 
6.00697 
6.1118 
2.71793 
2.8042 
2.89312 
2.98468 
3.07886 
3.17562 
3.27492 
3.37671 
3.48093 
3.5875 
3.69633 
3.80732 
3.92035 
4.03529 
4.152 
4.27032 
4.39008 
4.51108 
4.63312 
4.75599 
4.87945 
5.00326 
5.12715 
5.25085 
5.37409 
5.49656 
5.61796 
5.73797 
5.85627 
5.97253 
6.08643 
6.19763 
6.30581 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
1.07065
-0.0590121
-1.0872
-2.01308
-2.75455
-3.3886
-3.96107
-4.54461
-5.13649
-5.73462
-6.33743
-6.94377
-7.55273
-8.16367
-8.7761
-9.38963
-10.004
-10.619
-11.2344
-11.8502
-12.4663
-13.0825
-13.6989
-14.3154
-14.932
-15.5487
-16.1654
-16.7821
-17.3989
-18.0156
-18.6324
-19.2492
-19.866
-20.4829
-21.0997
-21.7165
-22.3333
-22.9502
-23.567
-24.1838
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd3.png');
clf
figure(2);
saveas(gcf,'oneResidualInd3.png');

N = [
4
8
16
32
];
E = [
-5.72948
-7.49913
-9.44757
-11.4354
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.1e-05
0.000134
0.007239
0.368182
];
T2 = [
0.002341
0.02535
0.392026
5.68756
];
figure(4);
subplot(3,1,3);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

figure(3);
title('Convergence rates');
legend('Dirichlet', 'Neumann', 'Mixed');
xlabel('log n');
ylabel('log of error');
saveas(gcf,'oneErrorInd1.png');
clf;
figure(4);
subplot(3,1,1);
title('Dirichlet');
subplot(3,1,2);
title('Neumann');
subplot(3,1,3);
title('Mixed');
saveas(gcf,'oneTimeInd1.png');
clf;

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0 
0.247404 
0.479426 
0.681639 
0.841471 
0.247404 
0.417216 
0.557063 
0.654338 
0.698985 
0.479426 
0.557063 
0.592069 
0.574483 
0.497495 
0.681639 
0.654338 
0.574483 
0.435406 
0.233986 
0.841471 
0.698985 
0.497495 
0.233986 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-3.76108
-7.66615
-11.5754
-15.4846
-19.3939
-23.3031
-27.2123
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0 
0.124675 
0.247404 
0.366273 
0.479426 
0.585097 
0.681639 
0.767544 
0.841471 
0.124675 
0.231803 
0.335065 
0.432606 
0.52266 
0.603578 
0.673851 
0.732134 
0.777268 
0.247404 
0.335065 
0.417 
0.491444 
0.556748 
0.611403 
0.654066 
0.683579 
0.698985 
0.366273 
0.432606 
0.491444 
0.541139 
0.580183 
0.607234 
0.621136 
0.620934 
0.605893 
0.479426 
0.52266 
0.556748 
0.580183 
0.591625 
0.589919 
0.574113 
0.543473 
0.497495 
0.585097 
0.603578 
0.611403 
0.607234 
0.589919 
0.558507 
0.512268 
0.450698 
0.373531 
0.681639 
0.673851 
0.654066 
0.621136 
0.574113 
0.512268 
0.435101 
0.342349 
0.233986 
0.767544 
0.732134 
0.683579 
0.620934 
0.543473 
0.450698 
0.342349 
0.218405 
0.0790858 
0.841471 
0.777268 
0.698985 
0.605893 
0.497495 
0.373531 
0.233986 
0.0790858 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-3.54624
-6.63237
-9.67003
-12.7814
-15.9231
-19.0778
-22.2381
-25.4008
-28.5647
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0 
0.0624593 
0.124675 
0.186403 
0.247404 
0.307439 
0.366273 
0.423676 
0.479426 
0.533303 
0.585097 
0.634607 
0.681639 
0.726009 
0.767544 
0.806081 
0.841471 
0.0624593 
0.12077 
0.178594 
0.23569 
0.291819 
0.346748 
0.400246 
0.45209 
0.502061 
0.54995 
0.595553 
0.638679 
0.679142 
0.716769 
0.751399 
0.782881 
0.811075 
0.124675 
0.178594 
0.231785 
0.284009 
0.335033 
0.384626 
0.432564 
0.47863 
0.522613 
0.564311 
0.60353 
0.640087 
0.673808 
0.704531 
0.732106 
0.756393 
0.777268 
0.186403 
0.23569 
0.284009 
0.331128 
0.376816 
0.420849 
0.46301 
0.503087 
0.540879 
0.576193 
0.608844 
0.638659 
0.665476 
0.689144 
0.709525 
0.726494 
0.739937 
0.247404 
0.291819 
0.335033 
0.376816 
0.416944 
0.4552 
0.491372 
0.525258 
0.556666 
0.585412 
0.611321 
0.634232 
0.653995 
0.67047 
0.683533 
0.693071 
0.698985 
0.307439 
0.346748 
0.384626 
0.420849 
0.4552 
0.487467 
0.517448 
0.54495 
0.56979 
0.591794 
0.6108 
0.626657 
0.639227 
0.648384 
0.654017 
0.656026 
0.654327 
0.366273 
0.400246 
0.432564 
0.46301 
0.491372 
0.517448 
0.541045 
0.56198 
0.580079 
0.595179 
0.607131 
0.615795 
0.621047 
0.622775 
0.620878 
0.615275 
0.605893 
0.423676 
0.45209 
0.47863 
0.503087 
0.525258 
0.54495 
0.56198 
0.576173 
0.587369 
0.595415 
0.600174 
0.601521 
0.599343 
0.593542 
0.584034 
0.570748 
0.553629 
0.479426 
0.502061 
0.522613 
0.540879 
0.556666 
0.56979 
0.580079 
0.587369 
0.59151 
0.592364 
0.589806 
0.583723 
0.574017 
0.560604 
0.543413 
0.52239 
0.497495 
0.533303 
0.54995 
0.564311 
0.576193 
0.585412 
0.591794 
0.595179 
0.595415 
0.592364 
0.585901 
0.575913 
0.562302 
0.544984 
0.523889 
0.498962 
0.470162 
0.437466 
0.585097 
0.595553 
0.60353 
0.608844 
0.611321 
0.6108 
0.607131 
0.600174 
0.589806 
0.575913 
0.558397 
0.537174 
0.512175 
0.483343 
0.45064 
0.414039 
0.373531 
0.634607 
0.638679 
0.640087 
0.638659 
0.634232 
0.626657 
0.615795 
0.601521 
0.583723 
0.562302 
0.537174 
0.50827 
0.475534 
0.438926 
0.398422 
0.354011 
0.305698 
0.681639 
0.679142 
0.673808 
0.665476 
0.653995 
0.639227 
0.621047 
0.599343 
0.574017 
0.544984 
0.512175 
0.475534 
0.435022 
0.390613 
0.342298 
0.290082 
0.233986 
0.726009 
0.716769 
0.704531 
0.689144 
0.67047 
0.648384 
0.622775 
0.593542 
0.560604 
0.523889 
0.483343 
0.438926 
0.390613 
0.338394 
0.282275 
0.222275 
0.158432 
0.767544 
0.751399 
0.732106 
0.709525 
0.683533 
0.654017 
0.620878 
0.584034 
0.543413 
0.498962 
0.45064 
0.398422 
0.342298 
0.282275 
0.218372 
0.150625 
0.0790858 
0.806081 
0.782881 
0.756393 
0.726494 
0.693071 
0.656026 
0.615275 
0.570748 
0.52239 
0.470162 
0.414039 
0.354011 
0.290082 
0.222275 
0.150625 
0.0751833 
-0.00398572 
0.841471 
0.811075 
0.777268 
0.739937 
0.698985 
0.654327 
0.605893 
0.553629 
0.497495 
0.437466 
0.373531 
0.305698 
0.233986 
0.158432 
0.0790858 
-0.00398572 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-3.40506
-6.53141
-9.46364
-12.4155
-15.3823
-18.3608
-21.3487
-24.344
-27.345
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0 
0.0312449 
0.0624593 
0.0936127 
0.124675 
0.155615 
0.186403 
0.21701 
0.247404 
0.277557 
0.307439 
0.33702 
0.366273 
0.395167 
0.423676 
0.451771 
0.479426 
0.506611 
0.533303 
0.559473 
0.585097 
0.61015 
0.634607 
0.658444 
0.681639 
0.704168 
0.726009 
0.747141 
0.767544 
0.787197 
0.806081 
0.824178 
0.841471 
0.0312449 
0.0614829 
0.0916598 
0.121745 
0.151709 
0.181521 
0.211151 
0.240569 
0.269745 
0.29865 
0.327255 
0.355531 
0.38345 
0.410982 
0.438101 
0.464778 
0.490988 
0.516702 
0.541896 
0.566544 
0.59062 
0.6141 
0.636961 
0.659179 
0.680731 
0.701596 
0.721751 
0.741177 
0.759854 
0.777761 
0.794882 
0.811198 
0.826692 
0.0624593 
0.0916598 
0.120769 
0.149756 
0.178592 
0.207245 
0.235686 
0.263886 
0.291815 
0.319443 
0.346743 
0.373685 
0.400241 
0.426383 
0.452084 
0.477317 
0.502055 
0.526272 
0.549943 
0.573043 
0.595547 
0.617431 
0.638672 
0.659248 
0.679136 
0.698315 
0.716764 
0.734464 
0.751395 
0.767539 
0.782878 
0.797395 
0.811075 
0.0936127 
0.121745 
0.149756 
0.177615 
0.205292 
0.232757 
0.25998 
0.286933 
0.313585 
0.339908 
0.365873 
0.391452 
0.416618 
0.441342 
0.465599 
0.48936 
0.512601 
0.535296 
0.557419 
0.578946 
0.599854 
0.620118 
0.639717 
0.658629 
0.676831 
0.694304 
0.711027 
0.726982 
0.742149 
0.756512 
0.770052 
0.782755 
0.794605 
0.124675 
0.151709 
0.178592 
0.205292 
0.23178 
0.258027 
0.284003 
0.309679 
0.335025 
0.360014 
0.384617 
0.408806 
0.432554 
0.455834 
0.478619 
0.500883 
0.522601 
0.543748 
0.564299 
0.58423 
0.603518 
0.62214 
0.640075 
0.657301 
0.673797 
0.689544 
0.704522 
0.718713 
0.732098 
0.744663 
0.756389 
0.767262 
0.777268 
0.155615 
0.181521 
0.207245 
0.232757 
0.258027 
0.283027 
0.307726 
0.332096 
0.356108 
0.379734 
0.402947 
0.425719 
0.448022 
0.469831 
0.491118 
0.51186 
0.53203 
0.551604 
0.570559 
0.58887 
0.606516 
0.623474 
0.639724 
0.655243 
0.670013 
0.684015 
0.697229 
0.709638 
0.721226 
0.731976 
0.741872 
0.750901 
0.759049 
0.186403 
0.211151 
0.235686 
0.25998 
0.284003 
0.307726 
0.331119 
0.354155 
0.376805 
0.399041 
0.420836 
0.442163 
0.462995 
0.483306 
0.503071 
0.522265 
0.540863 
0.558841 
0.576176 
0.592845 
0.608827 
0.6241 
0.638643 
0.652436 
0.665461 
0.677699 
0.689131 
0.699743 
0.709516 
0.718436 
0.726488 
0.73366 
0.739937 
0.21701 
0.240569 
0.263886 
0.286933 
0.309679 
0.332096 
0.354155 
0.375829 
0.397088 
0.417907 
0.438257 
0.458113 
0.477447 
0.496236 
0.514453 
0.532074 
0.549076 
0.565434 
0.581127 
0.596132 
0.610428 
0.623995 
0.636812 
0.64886 
0.660121 
0.670578 
0.680212 
0.689009 
0.696952 
0.704028 
0.710223 
0.715524 
0.719919 
0.247404 
0.269745 
0.291815 
0.313585 
0.335025 
0.356108 
0.376805 
0.397088 
0.41693 
0.436304 
0.455183 
0.473541 
0.491353 
0.508594 
0.525239 
0.541264 
0.556646 
0.571362 
0.585391 
0.59871 
0.6113 
0.623141 
0.634213 
0.644497 
0.653977 
0.662635 
0.670455 
0.677422 
0.683521 
0.68874 
0.693064 
0.696483 
0.698985 
0.277557 
0.29865 
0.319443 
0.339908 
0.360014 
0.379734 
0.399041 
0.417907 
0.436304 
0.454207 
0.471588 
0.488424 
0.504688 
0.520356 
0.535405 
0.54981 
0.56355 
0.576602 
0.588945 
0.600559 
0.611423 
0.621518 
0.630826 
0.639329 
0.647011 
0.653854 
0.659845 
0.664968 
0.66921 
0.672557 
0.675 
0.676525 
0.677124 
0.307439 
0.327255 
0.346743 
0.365873 
0.384617 
0.402947 
0.420836 
0.438257 
0.455183 
0.471588 
0.487447 
0.502735 
0.517427 
0.531499 
0.544928 
0.557691 
0.569767 
0.581133 
0.59177 
0.601658 
0.610777 
0.619108 
0.626635 
0.63334 
0.639207 
0.644221 
0.648367 
0.651632 
0.654004 
0.655469 
0.656018 
0.65564 
0.654327 
0.33702 
0.355531 
0.373685 
0.391452 
0.408806 
0.425719 
0.442163 
0.458113 
0.473541 
0.488424 
0.502735 
0.51645 
0.529546 
0.541998 
0.553785 
0.564884 
0.575274 
0.584935 
0.593846 
0.601988 
0.609343 
0.615893 
0.621622 
0.626512 
0.63055 
0.63372 
0.636008 
0.637403 
0.637892 
0.637465 
0.63611 
0.63382 
0.630586 
0.366273 
0.38345 
0.400241 
0.416618 
0.432554 
0.448022 
0.462995 
0.477447 
0.491353 
0.504688 
0.517427 
0.529546 
0.541022 
0.551832 
0.561955 
0.571368 
0.580052 
0.587987 
0.595152 
0.601531 
0.607105 
0.611857 
0.615771 
0.618832 
0.621025 
0.622337 
0.622756 
0.622268 
0.620864 
0.618533 
0.615267 
0.611056 
0.605893 
0.395167 
0.410982 
0.426383 
0.441342 
0.455834 
0.469831 
0.483306 
0.496236 
0.508594 
0.520356 
0.531499 
0.541998 
0.551832 
0.560978 
0.569415 
0.577123 
0.584081 
0.59027 
0.595672 
0.600269 
0.604045 
0.606982 
0.609067 
0.610284 
0.610619 
0.610061 
0.608597 
0.606217 
0.60291 
0.598666 
0.593479 
0.58734 
0.580243 
0.423676 
0.438101 
0.452084 
0.465599 
0.478619 
0.491118 
0.503071 
0.514453 
0.525239 
0.535405 
0.544928 
0.553785 
0.561955 
0.569415 
0.576146 
0.582128 
0.58734 
0.591766 
0.595387 
0.598186 
0.600147 
0.601255 
0.601495 
0.600854 
0.59932 
0.596879 
0.593523 
0.589239 
0.584019 
0.577855 
0.57074 
0.562666 
0.553629 
0.451771 
0.464778 
0.477317 
0.48936 
0.500883 
0.51186 
0.522265 
0.532074 
0.541264 
0.54981 
0.557691 
0.564884 
0.571368 
0.577123 
0.582128 
0.586364 
0.589813 
0.592457 
0.59428 
0.595264 
0.595396 
0.59466 
0.593042 
0.590531 
0.587115 
0.582781 
0.577521 
0.571325 
0.564184 
0.556092 
0.547042 
0.537029 
0.526048 
0.479426 
0.490988 
0.502055 
0.512601 
0.522601 
0.53203 
0.540863 
0.549076 
0.556646 
0.56355 
0.569767 
0.575274 
0.580052 
0.584081 
0.58734 
0.589813 
0.591481 
0.592327 
0.592335 
0.59149 
0.589777 
0.587183 
0.583696 
0.579303 
0.573993 
0.567756 
0.560583 
0.552467 
0.543398 
0.533372 
0.522382 
0.510424 
0.497495 
0.506611 
0.516702 
0.526272 
0.535296 
0.543748 
0.551604 
0.558841 
0.565434 
0.571362 
0.576602 
0.581133 
0.584935 
0.587987 
0.59027 
0.591766 
0.592457 
0.592327 
0.591358 
0.589537 
0.586848 
0.583277 
0.578813 
0.573444 
0.567157 
0.559944 
0.551795 
0.542702 
0.532657 
0.521654 
0.509688 
0.496754 
0.482848 
0.467968 
0.533303 
0.541896 
0.549943 
0.557419 
0.564299 
0.570559 
0.576176 
0.581127 
0.585391 
0.588945 
0.59177 
0.593846 
0.595152 
0.595672 
0.595387 
0.59428 
0.592335 
0.589537 
0.585871 
0.581324 
0.575884 
0.569538 
0.562275 
0.554085 
0.54496 
0.53489 
0.523869 
0.511889 
0.498947 
0.485036 
0.470154 
0.454298 
0.437466 
0.559473 
0.566544 
0.573043 
0.578946 
0.58423 
0.58887 
0.592845 
0.596132 
0.59871 
0.600559 
0.601658 
0.601988 
0.601531 
0.600269 
0.598186 
0.595264 
0.59149 
0.586848 
0.581324 
0.574907 
0.567585 
0.559345 
0.550179 
0.540077 
0.529031 
0.517033 
0.504078 
0.490159 
0.475272 
0.459413 
0.44258 
0.424772 
0.405987 
0.585097 
0.59062 
0.595547 
0.599854 
0.603518 
0.606516 
0.608827 
0.610428 
0.6113 
0.611423 
0.610777 
0.609343 
0.607105 
0.604045 
0.600147 
0.595396 
0.589777 
0.583277 
0.575884 
0.567585 
0.558369 
0.548226 
0.537148 
0.525125 
0.512151 
0.498219 
0.483323 
0.46746 
0.450625 
0.432816 
0.414031 
0.394269 
0.373531 
0.61015 
0.6141 
0.617431 
0.620118 
0.62214 
0.623474 
0.6241 
0.623995 
0.623141 
0.621518 
0.619108 
0.615893 
0.611857 
0.606982 
0.601255 
0.59466 
0.587183 
0.578813 
0.569538 
0.559345 
0.548226 
0.536171 
0.523172 
0.509222 
0.494313 
0.478441 
0.461601 
0.44379 
0.425004 
0.405243 
0.384505 
0.362791 
0.340101 
0.634607 
0.636961 
0.638672 
0.639717 
0.640075 
0.639724 
0.638643 
0.636812 
0.634213 
0.630826 
0.626635 
0.621622 
0.615771 
0.609067 
0.601495 
0.593042 
0.583696 
0.573444 
0.562275 
0.550179 
0.537148 
0.523172 
0.508245 
0.49236 
0.475512 
0.457695 
0.438908 
0.419146 
0.398408 
0.376693 
0.354003 
0.330337 
0.305698 
0.658444 
0.659179 
0.659248 
0.658629 
0.657301 
0.655243 
0.652436 
0.64886 
0.644497 
0.639329 
0.63334 
0.626512 
0.618832 
0.610284 
0.600854 
0.590531 
0.579303 
0.567157 
0.554085 
0.540077 
0.525125 
0.509222 
0.49236 
0.474535 
0.455742 
0.435978 
0.41524 
0.393526 
0.370835 
0.347168 
0.322525 
0.29691 
0.270325 
0.681639 
0.680731 
0.679136 
0.676831 
0.673797 
0.670013 
0.665461 
0.660121 
0.653977 
0.647011 
0.639207 
0.63055 
0.621025 
0.610619 
0.59932 
0.587115 
0.573993 
0.559944 
0.54496 
0.529031 
0.512151 
0.494313 
0.475512 
0.455742 
0.435002 
0.413287 
0.390596 
0.366929 
0.342286 
0.316667 
0.290075 
0.262514 
0.233986 
0.704168 
0.701596 
0.698315 
0.694304 
0.689544 
0.684015 
0.677699 
0.670578 
0.662635 
0.653854 
0.644221 
0.63372 
0.622337 
0.610061 
0.596879 
0.582781 
0.567756 
0.551795 
0.53489 
0.517033 
0.498219 
0.478441 
0.457695 
0.435978 
0.413287 
0.38962 
0.364976 
0.339356 
0.312761 
0.285193 
0.256655 
0.227151 
0.196686 
0.726009 
0.721751 
0.716764 
0.711027 
0.704522 
0.697229 
0.689131 
0.680212 
0.670455 
0.659845 
0.648367 
0.636008 
0.622756 
0.608597 
0.593523 
0.577521 
0.560583 
0.542702 
0.523869 
0.504078 
0.483323 
0.461601 
0.438908 
0.41524 
0.390596 
0.364976 
0.33838 
0.310808 
0.282264 
0.25275 
0.222269 
0.190828 
0.158432 
0.747141 
0.741177 
0.734464 
0.726982 
0.718713 
0.709638 
0.699743 
0.689009 
0.677422 
0.664968 
0.651632 
0.637403 
0.622268 
0.606217 
0.589239 
0.571325 
0.552467 
0.532657 
0.511889 
0.490159 
0.46746 
0.44379 
0.419146 
0.393526 
0.366929 
0.339356 
0.310808 
0.281288 
0.250797 
0.21934 
0.186922 
0.15355 
0.119229 
0.767544 
0.759854 
0.751395 
0.742149 
0.732098 
0.721226 
0.709516 
0.696952 
0.683521 
0.66921 
0.654004 
0.637892 
0.620864 
0.60291 
0.584019 
0.564184 
0.543398 
0.521654 
0.498947 
0.475272 
0.450625 
0.425004 
0.398408 
0.370835 
0.342286 
0.312761 
0.282264 
0.250797 
0.218364 
0.18497 
0.150621 
0.115323 
0.0790858 
0.787197 
0.777761 
0.767539 
0.756512 
0.744663 
0.731976 
0.718436 
0.704028 
0.68874 
0.672557 
0.655469 
0.637465 
0.618533 
0.598666 
0.577855 
0.556092 
0.533372 
0.509688 
0.485036 
0.459413 
0.432816 
0.405243 
0.376693 
0.347168 
0.316667 
0.285193 
0.25275 
0.21934 
0.18497 
0.149644 
0.113371 
0.0761568 
0.0380111 
0.806081 
0.794882 
0.782878 
0.770052 
0.756389 
0.741872 
0.726488 
0.710223 
0.693064 
0.675 
0.656018 
0.63611 
0.615267 
0.593479 
0.57074 
0.547042 
0.522382 
0.496754 
0.470154 
0.44258 
0.414031 
0.384505 
0.354003 
0.322525 
0.290075 
0.256655 
0.222269 
0.186922 
0.150621 
0.113371 
0.0751805 
0.0360585 
-0.00398572 
0.824178 
0.811198 
0.797395 
0.782755 
0.767262 
0.750901 
0.73366 
0.715524 
0.696483 
0.676525 
0.65564 
0.63382 
0.611056 
0.58734 
0.562666 
0.537029 
0.510424 
0.482848 
0.454298 
0.424772 
0.394269 
0.362791 
0.330337 
0.29691 
0.262514 
0.227151 
0.190828 
0.15355 
0.115323 
0.0761568 
0.0360585 
-0.00496198 
-0.0468941 
0.841471 
0.826692 
0.811075 
0.794605 
0.777268 
0.759049 
0.739937 
0.719919 
0.698985 
0.677124 
0.654327 
0.630586 
0.605893 
0.580243 
0.553629 
0.526048 
0.497495 
0.467968 
0.437466 
0.405987 
0.373531 
0.340101 
0.305698 
0.270325 
0.233986 
0.196686 
0.158432 
0.119229 
0.0790858 
0.0380111 
-0.00398572 
-0.0468941 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-3.32777
-6.49969
-9.40326
-12.3222
-15.2533
-18.194
-21.1426
-24.0977
-27.058
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd4.png');
clf
figure(2);
saveas(gcf,'oneResidualInd4.png');

N = [
4
8
16
32
];
E = [
-10.7072
-12.666
-14.6392
-16.6345
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.1e-05
0.000328
0.00613
0.377592
];
T2 = [
0.000733
0.007959
0.088724
1.28605
];
figure(4);
subplot(3,1,1);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0 
0.242139 
0.472522 
0.673639 
0.830728 
0.242631 
0.412282 
0.551586 
0.648472 
0.693187 
0.47449 
0.552844 
0.587865 
0.570293 
0.493791 
0.678505 
0.651534 
0.571551 
0.432423 
0.231334 
0.842101 
0.698053 
0.495759 
0.231826 
-0.0921764 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.965715
-1.25407
-1.47268
-1.71037
-1.952
-2.19459
-2.43743
-2.68034
-2.92327
-3.1662
-3.40914
-3.65208
-3.89502
-4.13796
-4.3809
-4.62383
-4.86677
-5.10971
-5.35265
-5.59559
-5.83853
-6.08147
-6.32441
-6.56735
-6.81029
-7.05322
-7.29616
-7.5391
-7.78204
-8.02498
-8.26792
-8.51086
-8.7538
-8.99674
-9.23967
-9.48261
-9.72555
-9.96849
-10.2114
-10.4544
-10.6973
-10.9402
-11.1832
-11.4261
-11.6691
-11.912
-12.1549
-12.3979
-12.6408
-12.8838
-13.1267
-13.3696
-13.6126
-13.8555
-14.0985
-14.3414
-14.5843
-14.8273
-15.0702
-15.3131
-15.5561
-15.799
-16.042
-16.2849
-16.5278
-16.7708
-17.0137
-17.2567
-17.4996
-17.7425
-17.9855
-18.2284
-18.4714
-18.7143
-18.9572
-19.2002
-19.4431
-19.686
-19.929
-20.1719
-20.4149
-20.6578
-20.9007
-21.1437
-21.3866
-21.6296
-21.8725
-22.1154
-22.3584
-22.6013
-22.8443
-23.0872
-23.3301
-23.5731
-23.816
-24.059
-24.3019
-24.5448
-24.7878
-25.0307
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0 
0.12317 
0.245376 
0.364044 
0.477126 
0.582781 
0.679313 
0.765154 
0.838793 
0.123184 
0.230103 
0.333143 
0.430553 
0.520546 
0.601445 
0.671719 
0.730012 
0.775192 
0.245433 
0.333186 
0.415093 
0.489496 
0.554778 
0.609433 
0.65212 
0.681688 
0.697211 
0.364174 
0.430667 
0.489565 
0.539278 
0.578333 
0.605404 
0.619344 
0.619212 
0.604291 
0.477362 
0.520761 
0.554937 
0.578417 
0.589887 
0.588209 
0.572444 
0.541869 
0.495991 
0.583164 
0.601794 
0.609704 
0.605581 
0.588293 
0.556905 
0.510698 
0.449176 
0.372078 
0.679915 
0.672244 
0.652518 
0.619615 
0.572603 
0.510766 
0.433613 
0.340887 
0.23256 
0.766131 
0.730763 
0.682213 
0.61956 
0.542083 
0.44929 
0.34093 
0.216995 
0.0777001 
0.840595 
0.776169 
0.697814 
0.604675 
0.496227 
0.372208 
0.232618 
0.0777145 
-0.0919322 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.891537
-1.20569
-1.40792
-1.54576
-1.70083
-1.86148
-2.02402
-2.18723
-2.35068
-2.51424
-2.67783
-2.84143
-3.00505
-3.16866
-3.33228
-3.49589
-3.65951
-3.82312
-3.98674
-4.15036
-4.31397
-4.47759
-4.64121
-4.80482
-4.96844
-5.13206
-5.29567
-5.45929
-5.62291
-5.78652
-5.95014
-6.11376
-6.27737
-6.44099
-6.60461
-6.76822
-6.93184
-7.09546
-7.25907
-7.42269
-7.58631
-7.74992
-7.91354
-8.07716
-8.24077
-8.40439
-8.56801
-8.73162
-8.89524
-9.05886
-9.22247
-9.38609
-9.54971
-9.71332
-9.87694
-10.0406
-10.2042
-10.3678
-10.5314
-10.695
-10.8586
-11.0223
-11.1859
-11.3495
-11.5131
-11.6767
-11.8403
-12.004
-12.1676
-12.3312
-12.4948
-12.6584
-12.822
-12.9857
-13.1493
-13.3129
-13.4765
-13.6401
-13.8037
-13.9674
-14.131
-14.2946
-14.4582
-14.6218
-14.7854
-14.9491
-15.1127
-15.2763
-15.4399
-15.6035
-15.7671
-15.9308
-16.0944
-16.258
-16.4216
-16.5852
-16.7488
-16.9125
-17.0761
-17.2397
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0 
0.0619684 
0.123983 
0.18561 
0.246552 
0.30655 
0.365361 
0.422751 
0.478493 
0.532368 
0.584164 
0.633677 
0.680713 
0.725088 
0.766625 
0.805157 
0.840514 
0.0619688 
0.120173 
0.177891 
0.234911 
0.290989 
0.345884 
0.39936 
0.45119 
0.501153 
0.549038 
0.594642 
0.63777 
0.678237 
0.71587 
0.750505 
0.781991 
0.810192 
0.123985 
0.177892 
0.23104 
0.283221 
0.334209 
0.383776 
0.431696 
0.47775 
0.521725 
0.56342 
0.602639 
0.639198 
0.672924 
0.703653 
0.731236 
0.755535 
0.776426 
0.185614 
0.234914 
0.283223 
0.330322 
0.375989 
0.420005 
0.462153 
0.502221 
0.540008 
0.575319 
0.60797 
0.637788 
0.664611 
0.688287 
0.708678 
0.72566 
0.739123 
0.246559 
0.290996 
0.334214 
0.375992 
0.416112 
0.454358 
0.490522 
0.524403 
0.555808 
0.584552 
0.610463 
0.633378 
0.653147 
0.66963 
0.682704 
0.692257 
0.698191 
0.306561 
0.345895 
0.383785 
0.420012 
0.454362 
0.486626 
0.516604 
0.544104 
0.568943 
0.590948 
0.609956 
0.625817 
0.638393 
0.647559 
0.653203 
0.655227 
0.653547 
0.365377 
0.399376 
0.43171 
0.462164 
0.490531 
0.516609 
0.540207 
0.561142 
0.579241 
0.594343 
0.606298 
0.614967 
0.620226 
0.621962 
0.620077 
0.614487 
0.605123 
0.422773 
0.451211 
0.477769 
0.502238 
0.524417 
0.544114 
0.561147 
0.575342 
0.58654 
0.594589 
0.599352 
0.600704 
0.598532 
0.592739 
0.583241 
0.569968 
0.552865 
0.478522 
0.501181 
0.521752 
0.540031 
0.555828 
0.568959 
0.579252 
0.586545 
0.59069 
0.591547 
0.588993 
0.582914 
0.573214 
0.559808 
0.542627 
0.521616 
0.496734 
0.532405 
0.549075 
0.563454 
0.57535 
0.584579 
0.590969 
0.59436 
0.5946 
0.591552 
0.585092 
0.575108 
0.561501 
0.544188 
0.5231 
0.49818 
0.469391 
0.436705 
0.584211 
0.594688 
0.602682 
0.608009 
0.610497 
0.609984 
0.60632 
0.599368 
0.589003 
0.575113 
0.5576 
0.536381 
0.511385 
0.482559 
0.449861 
0.413268 
0.372769 
0.633736 
0.637827 
0.639252 
0.637837 
0.63342 
0.625852 
0.614996 
0.600725 
0.58293 
0.561511 
0.536385 
0.507483 
0.47475 
0.438146 
0.397645 
0.353239 
0.304933 
0.680787 
0.678309 
0.67299 
0.664669 
0.653197 
0.638435 
0.62026 
0.598559 
0.573234 
0.544202 
0.511394 
0.474754 
0.434243 
0.389836 
0.341523 
0.28931 
0.233216 
0.725181 
0.715959 
0.703733 
0.688356 
0.669689 
0.647608 
0.622001 
0.59277 
0.559832 
0.523117 
0.48257 
0.438152 
0.389839 
0.337619 
0.2815 
0.221501 
0.157657 
0.766746 
0.750616 
0.731331 
0.708758 
0.68277 
0.653257 
0.62012 
0.583275 
0.542654 
0.4982 
0.449875 
0.397654 
0.341528 
0.281502 
0.217598 
0.14985 
0.0783082 
0.805325 
0.78213 
0.755646 
0.725749 
0.692328 
0.655284 
0.614533 
0.570005 
0.521644 
0.469412 
0.413284 
0.35325 
0.289316 
0.221505 
0.149851 
0.0744081 
-0.00476132 
0.840785 
0.81036 
0.776547 
0.739216 
0.698264 
0.653606 
0.60517 
0.552903 
0.496763 
0.436727 
0.372785 
0.304944 
0.233223 
0.157661 
0.07831 
-0.00476088 
-0.0914574 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.85206
-1.19082
-1.41295
-1.57848
-1.70107
-1.80332
-1.91305
-2.02607
-2.14056
-2.25572
-2.37117
-2.48677
-2.60243
-2.71811
-2.83381
-2.94952
-3.06523
-3.18095
-3.29666
-3.41238
-3.52809
-3.64381
-3.75952
-3.87524
-3.99095
-4.10667
-4.22238
-4.3381
-4.45381
-4.56953
-4.68524
-4.80096
-4.91667
-5.03239
-5.1481
-5.26382
-5.37953
-5.49525
-5.61096
-5.72668
-5.84239
-5.95811
-6.07382
-6.18954
-6.30525
-6.42097
-6.53668
-6.6524
-6.76811
-6.88383
-6.99954
-7.11526
-7.23097
-7.34669
-7.4624
-7.57812
-7.69383
-7.80955
-7.92527
-8.04098
-8.1567
-8.27241
-8.38813
-8.50384
-8.61956
-8.73527
-8.85099
-8.9667
-9.08242
-9.19813
-9.31385
-9.42956
-9.54528
-9.66099
-9.77671
-9.89242
-10.0081
-10.1239
-10.2396
-10.3553
-10.471
-10.5867
-10.7024
-10.8181
-10.9339
-11.0496
-11.1653
-11.281
-11.3967
-11.5124
-11.6281
-11.7439
-11.8596
-11.9753
-12.091
-12.2067
-12.3224
-12.4382
-12.5539
-12.6696
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0 
0.0308193 
0.0618455 
0.0928919 
0.123882 
0.15477 
0.185517 
0.216089 
0.246456 
0.276586 
0.306447 
0.336012 
0.365249 
0.394131 
0.422628 
0.450713 
0.478358 
0.505536 
0.532221 
0.558385 
0.584004 
0.609052 
0.633505 
0.657339 
0.680531 
0.703058 
0.724897 
0.746028 
0.766429 
0.786082 
0.804966 
0.823062 
0.84035 
0.0308193 
0.0609451 
0.0910116 
0.121013 
0.150913 
0.180675 
0.210265 
0.23965 
0.2688 
0.297682 
0.326267 
0.354526 
0.382429 
0.409948 
0.437056 
0.463723 
0.489923 
0.51563 
0.540817 
0.565459 
0.58953 
0.613005 
0.635862 
0.658077 
0.679626 
0.700488 
0.720642 
0.740067 
0.758742 
0.776649 
0.79377 
0.810085 
0.82558 
0.0618455 
0.0910116 
0.120063 
0.148993 
0.177778 
0.206389 
0.234795 
0.262965 
0.290869 
0.318475 
0.345756 
0.372681 
0.399222 
0.425351 
0.451041 
0.476264 
0.500993 
0.525203 
0.548867 
0.57196 
0.594459 
0.616339 
0.637576 
0.658148 
0.678033 
0.69721 
0.715657 
0.733356 
0.750286 
0.76643 
0.781769 
0.796287 
0.809969 
0.092892 
0.121013 
0.148993 
0.176815 
0.204455 
0.231886 
0.259079 
0.286005 
0.312634 
0.338937 
0.364884 
0.390448 
0.4156 
0.440312 
0.464557 
0.488309 
0.511541 
0.534228 
0.556344 
0.577866 
0.598768 
0.619028 
0.638623 
0.657531 
0.675731 
0.693201 
0.709923 
0.725876 
0.741043 
0.755405 
0.768946 
0.781651 
0.793503 
0.123882 
0.150913 
0.177778 
0.204455 
0.230917 
0.257138 
0.283089 
0.308742 
0.334069 
0.359039 
0.383626 
0.4078 
0.431535 
0.454803 
0.477578 
0.499833 
0.521542 
0.542682 
0.563226 
0.583151 
0.602434 
0.621052 
0.638983 
0.656205 
0.672699 
0.688443 
0.70342 
0.717609 
0.730995 
0.743559 
0.755286 
0.76616 
0.776168 
0.15477 
0.180675 
0.20639 
0.231886 
0.257138 
0.282118 
0.306797 
0.331148 
0.355143 
0.378754 
0.401952 
0.42471 
0.447001 
0.468799 
0.490077 
0.510809 
0.530971 
0.550539 
0.569487 
0.587793 
0.605434 
0.622387 
0.638633 
0.654149 
0.668917 
0.682916 
0.696129 
0.708537 
0.720124 
0.730874 
0.740771 
0.749802 
0.757952 
0.185517 
0.210265 
0.234796 
0.25908 
0.283089 
0.306797 
0.330175 
0.353196 
0.375831 
0.398053 
0.419835 
0.44115 
0.461971 
0.482273 
0.502028 
0.521214 
0.539804 
0.557775 
0.575104 
0.591768 
0.607745 
0.623014 
0.637553 
0.651344 
0.664366 
0.676601 
0.688033 
0.698643 
0.708416 
0.717336 
0.725389 
0.732562 
0.738842 
0.21609 
0.239651 
0.262966 
0.286006 
0.308743 
0.331149 
0.353196 
0.374857 
0.396105 
0.416911 
0.43725 
0.457095 
0.47642 
0.495199 
0.513408 
0.531022 
0.548016 
0.564368 
0.580055 
0.595055 
0.609347 
0.62291 
0.635723 
0.647769 
0.659027 
0.669482 
0.679115 
0.68791 
0.695854 
0.70293 
0.709126 
0.714428 
0.718826 
0.246457 
0.2688 
0.290869 
0.312635 
0.334069 
0.355144 
0.375831 
0.396105 
0.415937 
0.4353 
0.45417 
0.472519 
0.490322 
0.507554 
0.524191 
0.540209 
0.555585 
0.570295 
0.584319 
0.597633 
0.610219 
0.622056 
0.633124 
0.643406 
0.652884 
0.66154 
0.669358 
0.676325 
0.682424 
0.687642 
0.691968 
0.695388 
0.697892 
0.276586 
0.297682 
0.318476 
0.338938 
0.35904 
0.378754 
0.398054 
0.416911 
0.435301 
0.453195 
0.470568 
0.487396 
0.503652 
0.519313 
0.534355 
0.548754 
0.562488 
0.575534 
0.587872 
0.599481 
0.610341 
0.620433 
0.629738 
0.638239 
0.645918 
0.65276 
0.658749 
0.663871 
0.668113 
0.671461 
0.673904 
0.675431 
0.676032 
0.306448 
0.326268 
0.345756 
0.364885 
0.383626 
0.401952 
0.419836 
0.437251 
0.45417 
0.470569 
0.486421 
0.501701 
0.516386 
0.530452 
0.543874 
0.556632 
0.568702 
0.580064 
0.590696 
0.60058 
0.609694 
0.618023 
0.625546 
0.632249 
0.638114 
0.643126 
0.647271 
0.650536 
0.652907 
0.654373 
0.654923 
0.654547 
0.653235 
0.336013 
0.354527 
0.372682 
0.390449 
0.407801 
0.424711 
0.441151 
0.457096 
0.472519 
0.487396 
0.501701 
0.515411 
0.5285 
0.540947 
0.552728 
0.563822 
0.574208 
0.583864 
0.59277 
0.600909 
0.60826 
0.614807 
0.620533 
0.625421 
0.629457 
0.632625 
0.634913 
0.636307 
0.636796 
0.636368 
0.635015 
0.632726 
0.629494 
0.36525 
0.382431 
0.399223 
0.415601 
0.431536 
0.447002 
0.461972 
0.476421 
0.490323 
0.503653 
0.516387 
0.528501 
0.539971 
0.550777 
0.560895 
0.570304 
0.578983 
0.586913 
0.594075 
0.60045 
0.606021 
0.61077 
0.614681 
0.61774 
0.619931 
0.621242 
0.62166 
0.621172 
0.619767 
0.617437 
0.614171 
0.609961 
0.604801 
0.394132 
0.40995 
0.425353 
0.440313 
0.454805 
0.4688 
0.482274 
0.495201 
0.507555 
0.519314 
0.530452 
0.540948 
0.550777 
0.559919 
0.568352 
0.576055 
0.583009 
0.589195 
0.594593 
0.599187 
0.602959 
0.605894 
0.607976 
0.609191 
0.609525 
0.608966 
0.607501 
0.60512 
0.601812 
0.597569 
0.592382 
0.586245 
0.57915 
0.42263 
0.437058 
0.451043 
0.464559 
0.47758 
0.490078 
0.50203 
0.51341 
0.524193 
0.534356 
0.543875 
0.552729 
0.560895 
0.568352 
0.575079 
0.581057 
0.586266 
0.590688 
0.594306 
0.597102 
0.59906 
0.600165 
0.600404 
0.599761 
0.598225 
0.595783 
0.592425 
0.588141 
0.582921 
0.576757 
0.569642 
0.56157 
0.552535 
0.450715 
0.463725 
0.476266 
0.488311 
0.499835 
0.510811 
0.521216 
0.531023 
0.540211 
0.548755 
0.556633 
0.563823 
0.570304 
0.576056 
0.581057 
0.58529 
0.588736 
0.591377 
0.593197 
0.594178 
0.594307 
0.593569 
0.59195 
0.589437 
0.586018 
0.581684 
0.576423 
0.570226 
0.563085 
0.554993 
0.545944 
0.535932 
0.524952 
0.478361 
0.489926 
0.500996 
0.511544 
0.521545 
0.530974 
0.539806 
0.548018 
0.555587 
0.562489 
0.568704 
0.574209 
0.578984 
0.58301 
0.586267 
0.588736 
0.590401 
0.591244 
0.59125 
0.590402 
0.588687 
0.586091 
0.582602 
0.578207 
0.572895 
0.566657 
0.559484 
0.551366 
0.542298 
0.532272 
0.521282 
0.509326 
0.496398 
0.505539 
0.515633 
0.525206 
0.534231 
0.542684 
0.550541 
0.557778 
0.564371 
0.570297 
0.575536 
0.580066 
0.583865 
0.586915 
0.589196 
0.590689 
0.591378 
0.591245 
0.590274 
0.58845 
0.585758 
0.582186 
0.57772 
0.572348 
0.56606 
0.558846 
0.550695 
0.541601 
0.531555 
0.520552 
0.508586 
0.495652 
0.481748 
0.466869 
0.532224 
0.540821 
0.54887 
0.556348 
0.563229 
0.56949 
0.575107 
0.580058 
0.584321 
0.587875 
0.590698 
0.592772 
0.594077 
0.594594 
0.594307 
0.593197 
0.59125 
0.58845 
0.584782 
0.580233 
0.574791 
0.568443 
0.561178 
0.552987 
0.54386 
0.533789 
0.522766 
0.510787 
0.497844 
0.483933 
0.469051 
0.453196 
0.436365 
0.558389 
0.565463 
0.571964 
0.57787 
0.583155 
0.587796 
0.591771 
0.595058 
0.597636 
0.599484 
0.600582 
0.600911 
0.600452 
0.599188 
0.597103 
0.594179 
0.590403 
0.585759 
0.580234 
0.573815 
0.56649 
0.558249 
0.549081 
0.538977 
0.52793 
0.515931 
0.502974 
0.489054 
0.474167 
0.458308 
0.441476 
0.423668 
0.404884 
0.584009 
0.589534 
0.594463 
0.598772 
0.602438 
0.605437 
0.607749 
0.609351 
0.610222 
0.610344 
0.609697 
0.608262 
0.606023 
0.602961 
0.599061 
0.594309 
0.588688 
0.582187 
0.574791 
0.56649 
0.557272 
0.547128 
0.536048 
0.524024 
0.511048 
0.497115 
0.482218 
0.466354 
0.449518 
0.431709 
0.412924 
0.393163 
0.372426 
0.609057 
0.61301 
0.616343 
0.619033 
0.621056 
0.622392 
0.623018 
0.622914 
0.622059 
0.620436 
0.618026 
0.61481 
0.610772 
0.605896 
0.600167 
0.59357 
0.586093 
0.577721 
0.568443 
0.558249 
0.547128 
0.535071 
0.522071 
0.508119 
0.493209 
0.477335 
0.460494 
0.442682 
0.423896 
0.404134 
0.383396 
0.361682 
0.338994 
0.633511 
0.635868 
0.637581 
0.638629 
0.638988 
0.638638 
0.637558 
0.635728 
0.633128 
0.629742 
0.62555 
0.620536 
0.614684 
0.607979 
0.600406 
0.591951 
0.582603 
0.572349 
0.561179 
0.549081 
0.536048 
0.522071 
0.507142 
0.491256 
0.474406 
0.456588 
0.437799 
0.418036 
0.397298 
0.375583 
0.352892 
0.329226 
0.304588 
0.657346 
0.658083 
0.658154 
0.657537 
0.656211 
0.654155 
0.651349 
0.647773 
0.643411 
0.638243 
0.632252 
0.625424 
0.617743 
0.609194 
0.599763 
0.589439 
0.578208 
0.566061 
0.552988 
0.538978 
0.524024 
0.508119 
0.491256 
0.473429 
0.454635 
0.434869 
0.41413 
0.392415 
0.369723 
0.346055 
0.321413 
0.295797 
0.269212 
0.680538 
0.679633 
0.67804 
0.675738 
0.672705 
0.668923 
0.664372 
0.659033 
0.652888 
0.645922 
0.638118 
0.62946 
0.619935 
0.609528 
0.598227 
0.586021 
0.572897 
0.558847 
0.543861 
0.527931 
0.511049 
0.493209 
0.474406 
0.454635 
0.433893 
0.412177 
0.389485 
0.365816 
0.341172 
0.315553 
0.28896 
0.261398 
0.232871 
0.703066 
0.700497 
0.697218 
0.693209 
0.688451 
0.682923 
0.676608 
0.669487 
0.661545 
0.652764 
0.64313 
0.632629 
0.621246 
0.608969 
0.595786 
0.581686 
0.566659 
0.550697 
0.53379 
0.515932 
0.497116 
0.477336 
0.456589 
0.43487 
0.412177 
0.388508 
0.363863 
0.338242 
0.311646 
0.284077 
0.255538 
0.226034 
0.195569 
0.724907 
0.720652 
0.715667 
0.709932 
0.703428 
0.696136 
0.68804 
0.679121 
0.669364 
0.658754 
0.647276 
0.634917 
0.621663 
0.607504 
0.592428 
0.576425 
0.559486 
0.541603 
0.522768 
0.502975 
0.482219 
0.460495 
0.4378 
0.41413 
0.389485 
0.363863 
0.337266 
0.309693 
0.281147 
0.251631 
0.22115 
0.189708 
0.157312 
0.746039 
0.740078 
0.733366 
0.725886 
0.717618 
0.708545 
0.69865 
0.687917 
0.676331 
0.663877 
0.650541 
0.636311 
0.621176 
0.605123 
0.588144 
0.570228 
0.551369 
0.531557 
0.510788 
0.489056 
0.466355 
0.442683 
0.418037 
0.392415 
0.365817 
0.338242 
0.309693 
0.28017 
0.249678 
0.21822 
0.185802 
0.152428 
0.118107 
0.766442 
0.758755 
0.750298 
0.741054 
0.731005 
0.720133 
0.708424 
0.695861 
0.68243 
0.668118 
0.652912 
0.6368 
0.619772 
0.601816 
0.582924 
0.563088 
0.5423 
0.520554 
0.497845 
0.474168 
0.44952 
0.423897 
0.397299 
0.369724 
0.341172 
0.311646 
0.281147 
0.249678 
0.217244 
0.183848 
0.149498 
0.1142 
0.0779614 
0.786097 
0.776664 
0.766443 
0.755418 
0.74357 
0.730884 
0.717345 
0.702938 
0.687649 
0.671467 
0.654379 
0.636373 
0.617441 
0.597573 
0.57676 
0.554996 
0.532274 
0.508588 
0.483935 
0.45831 
0.43171 
0.404135 
0.375584 
0.346056 
0.315553 
0.284077 
0.251632 
0.21822 
0.183848 
0.148521 
0.112247 
0.0750314 
0.0368847 
0.804984 
0.793787 
0.781785 
0.76896 
0.755298 
0.740782 
0.725398 
0.709134 
0.691975 
0.67391 
0.654928 
0.63502 
0.614175 
0.592386 
0.569646 
0.545947 
0.521285 
0.495655 
0.469053 
0.441477 
0.412926 
0.383397 
0.352893 
0.321413 
0.288961 
0.255539 
0.221151 
0.185802 
0.149498 
0.112247 
0.0740549 
0.0349317 
-0.00511352 
0.823086 
0.810106 
0.796305 
0.781665 
0.766173 
0.749813 
0.732572 
0.714436 
0.695395 
0.675437 
0.654552 
0.632731 
0.609966 
0.586249 
0.561573 
0.535935 
0.509328 
0.48175 
0.453198 
0.423669 
0.393164 
0.361683 
0.329227 
0.295798 
0.261399 
0.226034 
0.189709 
0.152428 
0.1142 
0.0750315 
0.0349317 
-0.00608963 
-0.0480223 
0.840387 
0.825605 
0.809987 
0.793518 
0.776181 
0.757963 
0.738852 
0.718834 
0.6979 
0.676038 
0.653241 
0.629499 
0.604805 
0.579154 
0.552538 
0.524955 
0.4964 
0.466871 
0.436367 
0.404885 
0.372428 
0.338995 
0.304589 
0.269213 
0.232872 
0.195569 
0.157312 
0.118107 
0.0779615 
0.0368848 
-0.00511348 
-0.0480223 
-0.0918285 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.838399
-1.22256
-1.4828
-1.6685
-1.81098
-1.92898
-2.0276
-2.10434
-2.18608
-2.27042
-2.35612
-2.44252
-2.5293
-2.61627
-2.70334
-2.79046
-2.87761
-2.96477
-3.05193
-3.1391
-3.22627
-3.31344
-3.40061
-3.48778
-3.57495
-3.66212
-3.74929
-3.83646
-3.92363
-4.0108
-4.09798
-4.18515
-4.27232
-4.35949
-4.44666
-4.53383
-4.621
-4.70817
-4.79534
-4.88251
-4.96968
-5.05685
-5.14402
-5.23119
-5.31836
-5.40553
-5.4927
-5.57987
-5.66704
-5.75421
-5.84138
-5.92855
-6.01572
-6.10289
-6.19006
-6.27724
-6.36441
-6.45158
-6.53875
-6.62592
-6.71309
-6.80026
-6.88743
-6.9746
-7.06177
-7.14894
-7.23611
-7.32328
-7.41045
-7.49762
-7.58479
-7.67196
-7.75913
-7.8463
-7.93347
-8.02064
-8.10781
-8.19498
-8.28215
-8.36933
-8.4565
-8.54367
-8.63084
-8.71801
-8.80518
-8.89235
-8.97952
-9.06669
-9.15386
-9.24103
-9.3282
-9.41537
-9.50254
-9.58971
-9.67688
-9.76405
-9.85122
-9.93839
-10.0256
-10.1127
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd5.png');
clf
figure(2);
saveas(gcf,'oneResidualInd5.png');

N = [
4
8
16
32
];
E = [
-6.54048
-8.54486
-10.0292
-9.79173
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.2e-05
0.000133
0.006834
0.362136
];
T2 = [
0.010729
0.092587
1.01708
14.2033
];
figure(4);
subplot(3,1,2);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0.00105645 
0.24497 
0.476711 
0.679818 
0.841471 
0.245108 
0.415322 
0.555459 
0.653366 
0.698985 
0.477262 
0.555822 
0.591232 
0.574017 
0.497495 
0.681156 
0.654269 
0.574448 
0.43535 
0.233986 
0.844465 
0.700466 
0.498317 
0.234263 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-2.10763
-2.98112
-4.01621
-5.09905
-6.19203
-7.28733
-8.38318
-9.47917
-10.5752
-11.6712
-12.7673
-13.8633
-14.9593
-16.0554
-17.1514
-18.2474
-19.3435
-20.4395
-21.5355
-22.6315
-23.7276
-24.8236
-25.9196
-27.0157
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
-0.00107052 
0.123166 
0.245875 
0.364866 
0.478208 
0.584109 
0.680914 
0.76713 
0.841471 
0.123166 
0.230381 
0.333731 
0.431407 
0.521635 
0.60276 
0.673269 
0.731824 
0.777268 
0.245874 
0.333731 
0.415817 
0.490412 
0.555883 
0.610724 
0.653593 
0.683334 
0.698985 
0.364864 
0.431405 
0.490411 
0.540259 
0.579458 
0.606673 
0.620751 
0.620737 
0.605893 
0.478205 
0.521632 
0.555878 
0.579454 
0.591032 
0.589465 
0.573804 
0.543316 
0.497495 
0.584107 
0.602754 
0.610713 
0.606661 
0.589456 
0.558153 
0.512027 
0.450575 
0.373531 
0.680922 
0.673264 
0.653574 
0.620726 
0.57378 
0.512011 
0.434923 
0.342255 
0.233986 
0.767174 
0.731818 
0.683299 
0.620693 
0.543271 
0.450534 
0.342226 
0.218334 
0.0790858 
0.841654 
0.777238 
0.698915 
0.605821 
0.497423 
0.373457 
0.233908 
0.0790179 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.81487
-2.88354
-3.6947
-4.49543
-5.33413
-6.1901
-7.05412
-7.92197
-8.79164
-9.66219
-10.5332
-11.4044
-12.2757
-13.147
-14.0184
-14.8898
-15.7612
-16.6326
-17.504
-18.3754
-19.2468
-20.1182
-20.9896
-21.861
-22.7324
-23.6038
-24.4752
-25.3466
-26.218
-27.0894
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
-0.000483048 
0.0619213 
0.124134 
0.185879 
0.246903 
0.306966 
0.365832 
0.423269 
0.479054 
0.532968 
0.584801 
0.634351 
0.681424 
0.725839 
0.767421 
0.806013 
0.841471 
0.061921 
0.120245 
0.178082 
0.235196 
0.29135 
0.346306 
0.399834 
0.45171 
0.501715 
0.549639 
0.59528 
0.638443 
0.678947 
0.716618 
0.751293 
0.782825 
0.811075 
0.124133 
0.178081 
0.231295 
0.283543 
0.334592 
0.384212 
0.432179 
0.478276 
0.522291 
0.564023 
0.603277 
0.639871 
0.673631 
0.704395 
0.732012 
0.756345 
0.777268 
0.185876 
0.235194 
0.283541 
0.330686 
0.3764 
0.420461 
0.46265 
0.502757 
0.54058 
0.575926 
0.60861 
0.638461 
0.665314 
0.68902 
0.709441 
0.726451 
0.739937 
0.246898 
0.291345 
0.334588 
0.376398 
0.416553 
0.454836 
0.491036 
0.524951 
0.556389 
0.585165 
0.611106 
0.63405 
0.653847 
0.670358 
0.683457 
0.693032 
0.698985 
0.306959 
0.346299 
0.384205 
0.420456 
0.454833 
0.487127 
0.517135 
0.544665 
0.569533 
0.591566 
0.610602 
0.62649 
0.639092 
0.648282 
0.653948 
0.655991 
0.654327 
0.365821 
0.399823 
0.43217 
0.462642 
0.491029 
0.517132 
0.540755 
0.561716 
0.579841 
0.594969 
0.606948 
0.615642 
0.620923 
0.622681 
0.620815 
0.615243 
0.605893 
0.423254 
0.451695 
0.478262 
0.502745 
0.524941 
0.544658 
0.561712 
0.57593 
0.58715 
0.595222 
0.600007 
0.601381 
0.59923 
0.593457 
0.583976 
0.570719 
0.553629 
0.479034 
0.501696 
0.522273 
0.540563 
0.556374 
0.569521 
0.579832 
0.587145 
0.59131 
0.592188 
0.589653 
0.583595 
0.573914 
0.560526 
0.543361 
0.522364 
0.497495 
0.532943 
0.549614 
0.563999 
0.575904 
0.585145 
0.591549 
0.594955 
0.595212 
0.592182 
0.585741 
0.575774 
0.562186 
0.54489 
0.523818 
0.498915 
0.470139 
0.437466 
0.58477 
0.595249 
0.603248 
0.608582 
0.61108 
0.610579 
0.606929 
0.599992 
0.589642 
0.575769 
0.558273 
0.53707 
0.51209 
0.48328 
0.450597 
0.414018 
0.373531 
0.634313 
0.638406 
0.639835 
0.638426 
0.634018 
0.62646 
0.615616 
0.601359 
0.583578 
0.562174 
0.537063 
0.508177 
0.475459 
0.438869 
0.398383 
0.353991 
0.305698 
0.68138 
0.678903 
0.673587 
0.665272 
0.653807 
0.639055 
0.62089 
0.599201 
0.57389 
0.544872 
0.512077 
0.475452 
0.434955 
0.390562 
0.342264 
0.290065 
0.233986 
0.725787 
0.716566 
0.704343 
0.68897 
0.67031 
0.648237 
0.62264 
0.593421 
0.560495 
0.523792 
0.483259 
0.438855 
0.390555 
0.338349 
0.282244 
0.22226 
0.158432 
0.767362 
0.751233 
0.731952 
0.709382 
0.683401 
0.653895 
0.620767 
0.583933 
0.543322 
0.498881 
0.450568 
0.39836 
0.342247 
0.282235 
0.218344 
0.150611 
0.0790858 
0.80595 
0.782756 
0.756274 
0.726381 
0.692966 
0.655929 
0.615186 
0.570668 
0.522318 
0.470097 
0.413981 
0.353959 
0.290038 
0.222239 
0.150599 
0.0751683 
-0.00398572 
0.841416 
0.810992 
0.777181 
0.739855 
0.698908 
0.654256 
0.605828 
0.55357 
0.497441 
0.437416 
0.373486 
0.305656 
0.233948 
0.158398 
0.0790578 
-0.00400445 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.58229
-2.63427
-3.56941
-4.41559
-5.12053
-5.77552
-6.45433
-7.14759
-7.84981
-8.55767
-9.2691
-9.98282
-10.698
-11.4141
-12.1309
-12.848
-13.5654
-14.283
-15.0006
-15.7184
-16.4362
-17.154
-17.8718
-18.5897
-19.3075
-20.0254
-20.7433
-21.4611
-22.179
-22.8969
-23.6147
-24.3326
-25.0505
-25.7684
-26.4862
-27.2041
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
-0.000153174 
0.0310849 
0.062299 
0.0934543 
0.124519 
0.155463 
0.186255 
0.216866 
0.247264 
0.277421 
0.307308 
0.336894 
0.366151 
0.395051 
0.423565 
0.451665 
0.479324 
0.506515 
0.533212 
0.559388 
0.585017 
0.610075 
0.634538 
0.658381 
0.681581 
0.704116 
0.725963 
0.747102 
0.767511 
0.787171 
0.806063 
0.824168 
0.841471 
0.0310848 
0.0613245 
0.0915032 
0.121591 
0.151558 
0.181373 
0.211007 
0.240429 
0.269609 
0.298519 
0.327128 
0.355409 
0.383332 
0.410869 
0.437993 
0.464675 
0.490889 
0.516609 
0.541808 
0.566461 
0.590543 
0.614028 
0.636895 
0.659118 
0.680676 
0.701546 
0.721708 
0.74114 
0.759823 
0.777738 
0.794866 
0.811189 
0.826692 
0.0622988 
0.0915031 
0.120615 
0.149606 
0.178444 
0.207101 
0.235547 
0.26375 
0.291683 
0.319316 
0.34662 
0.373566 
0.400127 
0.426273 
0.451979 
0.477217 
0.50196 
0.526182 
0.549858 
0.572963 
0.595472 
0.617362 
0.638608 
0.659189 
0.679083 
0.698268 
0.716723 
0.734429 
0.751366 
0.767517 
0.782863 
0.797388 
0.811075 
0.0934541 
0.121591 
0.149606 
0.177468 
0.205149 
0.232617 
0.259844 
0.286801 
0.313457 
0.339784 
0.365754 
0.391337 
0.416507 
0.441237 
0.465498 
0.489264 
0.512509 
0.535209 
0.557337 
0.578869 
0.599782 
0.620052 
0.639656 
0.658573 
0.676781 
0.694259 
0.710988 
0.726949 
0.742122 
0.756491 
0.770039 
0.782748 
0.794605 
0.124519 
0.151558 
0.178444 
0.205148 
0.231641 
0.257891 
0.283871 
0.309551 
0.334901 
0.359894 
0.384501 
0.408695 
0.432447 
0.455731 
0.478521 
0.50079 
0.522513 
0.543664 
0.56422 
0.584156 
0.603449 
0.622076 
0.640016 
0.657247 
0.673749 
0.689501 
0.704485 
0.718681 
0.732073 
0.744643 
0.756376 
0.767255 
0.777268 
0.155462 
0.181373 
0.207101 
0.232617 
0.257891 
0.282894 
0.307597 
0.331971 
0.355988 
0.379618 
0.402835 
0.425611 
0.447918 
0.469731 
0.491024 
0.51177 
0.531944 
0.551523 
0.570482 
0.588799 
0.60645 
0.623413 
0.639667 
0.655192 
0.669967 
0.683974 
0.697194 
0.709609 
0.721202 
0.731957 
0.74186 
0.750895 
0.759049 
0.186254 
0.211006 
0.235546 
0.259844 
0.28387 
0.307597 
0.330994 
0.354034 
0.376688 
0.398928 
0.420727 
0.442058 
0.462895 
0.48321 
0.50298 
0.522178 
0.54078 
0.558762 
0.576102 
0.592776 
0.608763 
0.62404 
0.638588 
0.652387 
0.665417 
0.67766 
0.689098 
0.699714 
0.709493 
0.718418 
0.726477 
0.733654 
0.739937 
0.216864 
0.240427 
0.263749 
0.286799 
0.30955 
0.331971 
0.354034 
0.375711 
0.396975 
0.417797 
0.438152 
0.458011 
0.47735 
0.496143 
0.514364 
0.53199 
0.548996 
0.565359 
0.581056 
0.596066 
0.610367 
0.623938 
0.63676 
0.648813 
0.660079 
0.67054 
0.68018 
0.688982 
0.69693 
0.704012 
0.710212 
0.715518 
0.719919 
0.247262 
0.269608 
0.291682 
0.313455 
0.3349 
0.355986 
0.376687 
0.396974 
0.41682 
0.436198 
0.455081 
0.473443 
0.491259 
0.508504 
0.525153 
0.541182 
0.556568 
0.571289 
0.585322 
0.598646 
0.611241 
0.623086 
0.634162 
0.644452 
0.653936 
0.662599 
0.670424 
0.677396 
0.683501 
0.688724 
0.693054 
0.696477 
0.698985 
0.277419 
0.298517 
0.319314 
0.339782 
0.359892 
0.379616 
0.398927 
0.417796 
0.436198 
0.454104 
0.47149 
0.488329 
0.504597 
0.520269 
0.535322 
0.549732 
0.563476 
0.576532 
0.588879 
0.600497 
0.611366 
0.621465 
0.630778 
0.639286 
0.646972 
0.65382 
0.659815 
0.664943 
0.66919 
0.672542 
0.674989 
0.67652 
0.677124 
0.307305 
0.327126 
0.346617 
0.365751 
0.384499 
0.402833 
0.420726 
0.43815 
0.45508 
0.471489 
0.487352 
0.502643 
0.517339 
0.531415 
0.544848 
0.557615 
0.569695 
0.581066 
0.591707 
0.601598 
0.610721 
0.619057 
0.626588 
0.633298 
0.639169 
0.644188 
0.648339 
0.651609 
0.653985 
0.655455 
0.656009 
0.655636 
0.654327 
0.336891 
0.355406 
0.373563 
0.391334 
0.408692 
0.425608 
0.442056 
0.458009 
0.473442 
0.488328 
0.502643 
0.516362 
0.529461 
0.541917 
0.553708 
0.564811 
0.575205 
0.58487 
0.593785 
0.601931 
0.60929 
0.615844 
0.621577 
0.626472 
0.630514 
0.633688 
0.635981 
0.63738 
0.637874 
0.637451 
0.636101 
0.633815 
0.630586 
0.366147 
0.383328 
0.400123 
0.416504 
0.432443 
0.447915 
0.462892 
0.477348 
0.491257 
0.504595 
0.517338 
0.52946 
0.54094 
0.551754 
0.56188 
0.571298 
0.579986 
0.587924 
0.595094 
0.601476 
0.607054 
0.61181 
0.615728 
0.618793 
0.62099 
0.622307 
0.62273 
0.622247 
0.620847 
0.61852 
0.615258 
0.611051 
0.605893 
0.395046 
0.410864 
0.426269 
0.441232 
0.455727 
0.469727 
0.483207 
0.49614 
0.508501 
0.520267 
0.531413 
0.541916 
0.551753 
0.560903 
0.569344 
0.577055 
0.584017 
0.59021 
0.595616 
0.600216 
0.603996 
0.606937 
0.609026 
0.610246 
0.610586 
0.610032 
0.608572 
0.606196 
0.602893 
0.598654 
0.59347 
0.587336 
0.580243 
0.423559 
0.437987 
0.451974 
0.465492 
0.478516 
0.491019 
0.502975 
0.51436 
0.525149 
0.535319 
0.544845 
0.553706 
0.561879 
0.569343 
0.576078 
0.582063 
0.587279 
0.591708 
0.595332 
0.598135 
0.6001 
0.601211 
0.601456 
0.600819 
0.599288 
0.596852 
0.593499 
0.589219 
0.584003 
0.577843 
0.570732 
0.562662 
0.553629 
0.451659 
0.464669 
0.477211 
0.489258 
0.500784 
0.511764 
0.522172 
0.531985 
0.541178 
0.549727 
0.557612 
0.564808 
0.571296 
0.577054 
0.582062 
0.586302 
0.589754 
0.592402 
0.594228 
0.595216 
0.595351 
0.594618 
0.593005 
0.590497 
0.587084 
0.582754 
0.577498 
0.571306 
0.564169 
0.556081 
0.547035 
0.537025 
0.526048 
0.479317 
0.490882 
0.501953 
0.512502 
0.522506 
0.531938 
0.540774 
0.54899 
0.556563 
0.563471 
0.56969 
0.575201 
0.579983 
0.584014 
0.587277 
0.589753 
0.591424 
0.592273 
0.592285 
0.591443 
0.589734 
0.587144 
0.58366 
0.57927 
0.573964 
0.56773 
0.560561 
0.552448 
0.543383 
0.533361 
0.522375 
0.510421 
0.497495 
0.506507 
0.516601 
0.526174 
0.535201 
0.543656 
0.551515 
0.558755 
0.565352 
0.571283 
0.576526 
0.58106 
0.584865 
0.58792 
0.590206 
0.591706 
0.5924 
0.592273 
0.591307 
0.589489 
0.586803 
0.583236 
0.578776 
0.573409 
0.567126 
0.559916 
0.551771 
0.542681 
0.532639 
0.52164 
0.509677 
0.496747 
0.482845 
0.467968 
0.533202 
0.541799 
0.549849 
0.557328 
0.564211 
0.570474 
0.576094 
0.581048 
0.585315 
0.588872 
0.591701 
0.593779 
0.595089 
0.595611 
0.595329 
0.594225 
0.592283 
0.589488 
0.585826 
0.581282 
0.575845 
0.569502 
0.562242 
0.554055 
0.544933 
0.534867 
0.523849 
0.511873 
0.498933 
0.485026 
0.470147 
0.454294 
0.437466 
0.559377 
0.566451 
0.572953 
0.578859 
0.584146 
0.588789 
0.592767 
0.596057 
0.598638 
0.600489 
0.601591 
0.601924 
0.60147 
0.600211 
0.598131 
0.595212 
0.59144 
0.586801 
0.581281 
0.574867 
0.567547 
0.559311 
0.550148 
0.540049 
0.529006 
0.517011 
0.504059 
0.490143 
0.475259 
0.459403 
0.442574 
0.424769 
0.405987 
0.585005 
0.590531 
0.595461 
0.599771 
0.603438 
0.606439 
0.608752 
0.610357 
0.611231 
0.611357 
0.610713 
0.609282 
0.607047 
0.603989 
0.600094 
0.595346 
0.58973 
0.583233 
0.575843 
0.567546 
0.558333 
0.548194 
0.537118 
0.525098 
0.512127 
0.498198 
0.483305 
0.467445 
0.450613 
0.432807 
0.414025 
0.394266 
0.373531 
0.610062 
0.614016 
0.617349 
0.620039 
0.622064 
0.623401 
0.624029 
0.623927 
0.623075 
0.621455 
0.619048 
0.615836 
0.611802 
0.60693 
0.601205 
0.594612 
0.587139 
0.578772 
0.569499 
0.559309 
0.548193 
0.53614 
0.523144 
0.509196 
0.49429 
0.478421 
0.461584 
0.443775 
0.424993 
0.405234 
0.384499 
0.362788 
0.340101 
0.634524 
0.636881 
0.638594 
0.639642 
0.640003 
0.639654 
0.638575 
0.636747 
0.634151 
0.630767 
0.626578 
0.621567 
0.615719 
0.609017 
0.601448 
0.592998 
0.583654 
0.573404 
0.562238 
0.550145 
0.537116 
0.523143 
0.508218 
0.492336 
0.47549 
0.457676 
0.438891 
0.419132 
0.398397 
0.376685 
0.353997 
0.330334 
0.305698 
0.658365 
0.659103 
0.659174 
0.658558 
0.657232 
0.655177 
0.652373 
0.648799 
0.644439 
0.639273 
0.633286 
0.626461 
0.618782 
0.610237 
0.60081 
0.590489 
0.579263 
0.56712 
0.55405 
0.540045 
0.525095 
0.509194 
0.492335 
0.474512 
0.455722 
0.43596 
0.415224 
0.393513 
0.370824 
0.34716 
0.32252 
0.296907 
0.270325 
0.681564 
0.680659 
0.679066 
0.676764 
0.673732 
0.669951 
0.665401 
0.660064 
0.653922 
0.646958 
0.639156 
0.630501 
0.620979 
0.610575 
0.599278 
0.587075 
0.573955 
0.559909 
0.544927 
0.529 
0.512122 
0.494287 
0.475488 
0.455721 
0.434982 
0.41327 
0.390581 
0.366917 
0.342276 
0.316659 
0.29007 
0.262511 
0.233986 
0.704097 
0.701528 
0.698249 
0.694241 
0.689483 
0.683956 
0.677643 
0.670524 
0.662583 
0.653805 
0.644173 
0.633674 
0.622294 
0.61002 
0.59684 
0.582744 
0.567721 
0.551762 
0.534859 
0.517004 
0.498192 
0.478416 
0.457673 
0.435958 
0.413268 
0.389604 
0.364962 
0.339345 
0.312752 
0.285186 
0.25665 
0.227149 
0.196686 
0.725943 
0.721688 
0.716703 
0.710968 
0.704465 
0.697175 
0.689079 
0.680162 
0.670407 
0.659799 
0.648323 
0.635966 
0.622715 
0.608559 
0.593486 
0.577486 
0.560551 
0.542671 
0.52384 
0.504051 
0.483298 
0.461578 
0.438886 
0.41522 
0.390579 
0.364961 
0.338367 
0.310797 
0.282255 
0.252743 
0.222265 
0.190826 
0.158432 
0.74708 
0.741118 
0.734407 
0.726927 
0.71866 
0.709588 
0.699694 
0.688962 
0.677377 
0.664925 
0.651591 
0.637364 
0.622231 
0.606181 
0.589205 
0.571293 
0.552436 
0.532628 
0.511863 
0.490133 
0.467437 
0.443768 
0.419126 
0.393507 
0.366913 
0.339342 
0.310796 
0.281277 
0.250788 
0.219334 
0.186918 
0.153548 
0.119229 
0.767487 
0.759799 
0.751343 
0.742099 
0.73205 
0.721179 
0.709471 
0.696909 
0.68348 
0.66917 
0.653966 
0.637856 
0.62083 
0.602877 
0.583988 
0.564155 
0.54337 
0.521628 
0.498922 
0.475248 
0.450603 
0.424984 
0.398389 
0.370818 
0.34227 
0.312748 
0.282252 
0.250787 
0.218355 
0.184963 
0.150616 
0.115321 
0.0790858 
0.787145 
0.777712 
0.767491 
0.756466 
0.744618 
0.731933 
0.718395 
0.703989 
0.688702 
0.672521 
0.655435 
0.637432 
0.618502 
0.598637 
0.577827 
0.556065 
0.533346 
0.509664 
0.485013 
0.459392 
0.432796 
0.405224 
0.376676 
0.347152 
0.316653 
0.28518 
0.252738 
0.21933 
0.184962 
0.149638 
0.113366 
0.0761546 
0.0380111 
0.806035 
0.794838 
0.782835 
0.770011 
0.756349 
0.741834 
0.726451 
0.710188 
0.69303 
0.674967 
0.655987 
0.636081 
0.615238 
0.593452 
0.570714 
0.547018 
0.522359 
0.496732 
0.470133 
0.442561 
0.414013 
0.384488 
0.353987 
0.322511 
0.290062 
0.256643 
0.222258 
0.186913 
0.150613 
0.113364 
0.0751761 
0.0360561 
-0.00398572 
0.824139 
0.811159 
0.797357 
0.782718 
0.767226 
0.750867 
0.733626 
0.715492 
0.696452 
0.676496 
0.655613 
0.633794 
0.61103 
0.587316 
0.562643 
0.537007 
0.510404 
0.482828 
0.454279 
0.424754 
0.394253 
0.362775 
0.330322 
0.296896 
0.262501 
0.22714 
0.190817 
0.15354 
0.115315 
0.0761503 
0.0360537 
-0.00496462 
-0.0468941 
0.841442 
0.826659 
0.811042 
0.794572 
0.777236 
0.759019 
0.739908 
0.719891 
0.698958 
0.677098 
0.654302 
0.630562 
0.605871 
0.580222 
0.553609 
0.526029 
0.497477 
0.467951 
0.437449 
0.405971 
0.373516 
0.340087 
0.305685 
0.270312 
0.233974 
0.196675 
0.158421 
0.11922 
0.0790775 
0.038004 
-0.00399126 
-0.0468975 
-0.0907026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.40126
-2.38791
-3.29826
-4.14788
-4.95192
-5.71568
-6.4427
-7.13302
-7.69334
-8.26496
-8.84897
-9.44179
-10.041
-10.6448
-11.252
-11.8616
-12.4731
-13.086
-13.6999
-14.3145
-14.9297
-15.5453
-16.1612
-16.7774
-17.3937
-18.0101
-18.6267
-19.2433
-19.86
-20.4767
-21.0934
-21.7102
-22.327
-22.9438
-23.5606
-24.1774
-24.7942
-25.4111
-26.0279
-26.6447
-27.2616
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd6.png');
clf
figure(2);
saveas(gcf,'oneResidualInd6.png');

N = [
4
8
16
32
];
E = [
-8.3835
-9.35193
-10.8507
-12.6054
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.2e-05
0.000335
0.006619
0.372852
];
T2 = [
0.00236
0.031949
0.349658
5.70905
];
figure(4);
subplot(3,1,3);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

figure(3);
title('Convergence rates');
legend('Dirichlet', 'Neumann', 'Mixed');
xlabel('log n');
ylabel('log of error');
saveas(gcf,'oneErrorInd2.png');
clf;
figure(4);
subplot(3,1,1);
title('Dirichlet');
subplot(3,1,2);
title('Neumann');
subplot(3,1,3);
title('Mixed');
saveas(gcf,'oneTimeInd2.png');
clf;

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0 
0.247404 
0.479426 
0.681639 
0.841471 
0.247404 
0.557467 
0.852067 
1.11675 
1.33887 
0.479426 
0.852067 
1.2092 
1.53636 
1.8209 
0.681639 
1.11675 
1.53636 
1.92604 
2.27311 
0.841471 
1.33887 
1.8209 
2.27311 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-2.62477
-6.5297
-10.4389
-14.3482
-18.2574
-22.1666
-26.0759
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0 
0.124675 
0.247404 
0.366273 
0.479426 
0.585097 
0.681639 
0.767544 
0.841471 
0.124675 
0.264987 
0.403352 
0.537853 
0.666635 
0.787933 
0.900095 
1.00161 
1.09115 
0.247404 
0.403352 
0.557349 
0.70748 
0.851891 
0.988813 
1.1166 
1.23373 
1.33887 
0.366273 
0.537853 
0.70748 
0.87324 
1.03328 
1.18582 
1.32923 
1.46199 
1.58274 
0.479426 
0.666635 
0.851891 
1.03328 
1.20894 
1.37711 
1.53614 
1.68452 
1.8209 
0.585097 
0.787933 
0.988813 
1.18582 
1.37711 
1.56091 
1.73556 
1.89957 
2.05157 
0.681639 
0.900095 
1.1166 
1.32923 
1.53614 
1.73556 
1.92585 
2.10548 
2.27311 
0.767544 
1.00161 
1.23373 
1.46199 
1.68452 
1.89957 
2.10548 
2.30074 
2.48401 
0.841471 
1.09115 
1.33887 
1.58274 
1.8209 
2.05157 
2.27311 
2.48401 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.98126
-5.27085
-8.43648
-11.6365
-14.8118
-17.9654
-21.1252
-24.2877
-27.4515
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0 
0.0624593 
0.124675 
0.186403 
0.247404 
0.307439 
0.366273 
0.423676 
0.479426 
0.533303 
0.585097 
0.634607 
0.681639 
0.726009 
0.767544 
0.806081 
0.841471 
0.0624593 
0.128826 
0.194948 
0.260584 
0.325491 
0.389433 
0.452173 
0.513484 
0.57314 
0.630923 
0.686624 
0.74004 
0.790977 
0.839253 
0.884693 
0.927136 
0.96643 
0.124675 
0.194948 
0.264978 
0.33452 
0.403334 
0.471183 
0.53783 
0.603047 
0.666609 
0.728299 
0.787906 
0.845228 
0.900072 
0.952253 
1.0016 
1.04795 
1.09115 
0.186403 
0.260584 
0.33452 
0.407969 
0.48069 
0.552445 
0.622999 
0.692123 
0.759591 
0.825187 
0.888701 
0.949929 
1.00868 
1.06477 
1.11802 
1.16827 
1.21537 
0.247404 
0.325491 
0.403334 
0.48069 
0.557318 
0.63298 
0.70744 
0.78047 
0.851845 
0.921347 
0.988767 
1.0539 
1.11656 
1.17655 
1.23371 
1.28787 
1.33887 
0.307439 
0.389433 
0.471183 
0.552445 
0.63298 
0.712547 
0.790914 
0.867851 
0.943132 
1.01654 
1.08787 
1.15691 
1.22347 
1.28737 
1.34843 
1.40649 
1.46141 
0.366273 
0.452173 
0.53783 
0.622999 
0.70744 
0.790914 
0.873188 
0.95403 
1.03322 
1.11053 
1.18576 
1.25871 
1.32918 
1.39698 
1.46195 
1.52392 
1.58274 
0.423676 
0.513484 
0.603047 
0.692123 
0.78047 
0.867851 
0.95403 
1.03878 
1.12187 
1.20309 
1.28223 
1.35909 
1.43346 
1.50517 
1.57404 
1.63992 
1.70265 
0.479426 
0.57314 
0.666609 
0.759591 
0.851845 
0.943132 
1.03322 
1.12187 
1.20887 
1.294 
1.37705 
1.4578 
1.53608 
1.6117 
1.68448 
1.75426 
1.8209 
0.533303 
0.630923 
0.728299 
0.825187 
0.921347 
1.01654 
1.11053 
1.20309 
1.294 
1.38303 
1.46999 
1.55465 
1.63684 
1.71636 
1.79305 
1.86673 
1.93727 
0.585097 
0.686624 
0.787906 
0.888701 
0.988767 
1.08787 
1.18576 
1.28223 
1.37705 
1.46999 
1.56084 
1.64941 
1.73551 
1.81893 
1.89953 
1.97712 
2.05157 
0.634607 
0.74004 
0.845228 
0.949929 
1.0539 
1.15691 
1.25871 
1.35909 
1.4578 
1.55465 
1.64941 
1.74189 
1.83189 
1.91923 
2.00373 
2.08523 
2.16358 
0.681639 
0.790977 
0.900072 
1.00868 
1.11656 
1.22347 
1.32918 
1.43346 
1.53608 
1.63684 
1.73551 
1.83189 
1.92579 
2.01704 
2.10544 
2.19085 
2.27311 
0.726009 
0.839253 
0.952253 
1.06477 
1.17655 
1.28737 
1.39698 
1.50517 
1.6117 
1.71636 
1.81893 
1.91923 
2.01704 
2.11219 
2.2045 
2.29381 
2.37998 
0.767544 
0.884693 
1.0016 
1.11802 
1.23371 
1.34843 
1.46195 
1.57404 
1.68448 
1.79305 
1.89953 
2.00373 
2.10544 
2.2045 
2.30072 
2.39394 
2.48401 
0.806081 
0.927136 
1.04795 
1.16827 
1.28787 
1.40649 
1.52392 
1.63992 
1.75426 
1.86673 
1.97712 
2.08523 
2.19085 
2.29381 
2.39394 
2.49107 
2.58505 
0.841471 
0.96643 
1.09115 
1.21537 
1.33887 
1.46141 
1.58274 
1.70265 
1.8209 
1.93727 
2.05157 
2.16358 
2.27311 
2.37998 
2.48401 
2.58505 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.7583
-4.97788
-8.11418
-11.1788
-14.1728
-17.1784
-20.1762
-23.1814
-26.1921
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0 
0.0312449 
0.0624593 
0.0936127 
0.124675 
0.155615 
0.186403 
0.21701 
0.247404 
0.277557 
0.307439 
0.33702 
0.366273 
0.395167 
0.423676 
0.451771 
0.479426 
0.506611 
0.533303 
0.559473 
0.585097 
0.61015 
0.634607 
0.658444 
0.681639 
0.704168 
0.726009 
0.747141 
0.767544 
0.787197 
0.806081 
0.824178 
0.841471 
0.0312449 
0.0634664 
0.0956575 
0.127787 
0.159826 
0.191743 
0.223508 
0.255091 
0.286462 
0.317591 
0.34845 
0.379008 
0.409237 
0.439108 
0.468594 
0.497665 
0.526296 
0.554459 
0.582126 
0.609273 
0.635874 
0.661903 
0.687337 
0.712151 
0.736322 
0.759827 
0.782645 
0.804753 
0.826133 
0.846762 
0.866623 
0.885697 
0.903966 
0.0624593 
0.0956575 
0.128825 
0.161932 
0.194947 
0.22784 
0.260582 
0.293141 
0.325489 
0.357595 
0.38943 
0.420965 
0.45217 
0.483018 
0.51348 
0.543529 
0.573136 
0.602275 
0.630919 
0.659043 
0.68662 
0.713626 
0.740036 
0.765827 
0.790974 
0.815456 
0.83925 
0.862335 
0.884691 
0.906297 
0.927135 
0.947185 
0.96643 
0.0936127 
0.127787 
0.161932 
0.196015 
0.230007 
0.263877 
0.297595 
0.331131 
0.364455 
0.397538 
0.430349 
0.462861 
0.495043 
0.526868 
0.558306 
0.589331 
0.619915 
0.650031 
0.679652 
0.708752 
0.737306 
0.765288 
0.792675 
0.819442 
0.845566 
0.871024 
0.895795 
0.919856 
0.943189 
0.965771 
0.987585 
1.00861 
1.02883 
0.124675 
0.159826 
0.194947 
0.230007 
0.264975 
0.299822 
0.334517 
0.369029 
0.40333 
0.437389 
0.471177 
0.504665 
0.537824 
0.570625 
0.603041 
0.635042 
0.666602 
0.697695 
0.728292 
0.758369 
0.787899 
0.816858 
0.845221 
0.872965 
0.900066 
0.9265 
0.952248 
0.977286 
1.00159 
1.02515 
1.04794 
1.06995 
1.09115 
0.155615 
0.191743 
0.22784 
0.263877 
0.299822 
0.335645 
0.371317 
0.406806 
0.442083 
0.477119 
0.511884 
0.546348 
0.580484 
0.614261 
0.647653 
0.680631 
0.713168 
0.745237 
0.776811 
0.807864 
0.838371 
0.868307 
0.897647 
0.926367 
0.954444 
0.981855 
1.00858 
1.03459 
1.05988 
1.08441 
1.10818 
1.13116 
1.15334 
0.186403 
0.223508 
0.260582 
0.297595 
0.334517 
0.371317 
0.407964 
0.44443 
0.480684 
0.516697 
0.552438 
0.587879 
0.622991 
0.657745 
0.692114 
0.726068 
0.759582 
0.792627 
0.825178 
0.857208 
0.888691 
0.919603 
0.94992 
0.979616 
1.00867 
1.03706 
1.06476 
1.09175 
1.11801 
1.14352 
1.16827 
1.19222 
1.21537 
0.21701 
0.255091 
0.293141 
0.331131 
0.369029 
0.406806 
0.44443 
0.481873 
0.519103 
0.556092 
0.59281 
0.629228 
0.665316 
0.701047 
0.736392 
0.771324 
0.805814 
0.839836 
0.873363 
0.906369 
0.938829 
0.970718 
1.00201 
1.03268 
1.06271 
1.09208 
1.12076 
1.14872 
1.17596 
1.20245 
1.22817 
1.2531 
1.27723 
0.247404 
0.286462 
0.325489 
0.364455 
0.40333 
0.442083 
0.480684 
0.519103 
0.55731 
0.595276 
0.63297 
0.670365 
0.70743 
0.744137 
0.780459 
0.816367 
0.851833 
0.886832 
0.921336 
0.955319 
0.988755 
1.02162 
1.05389 
1.08554 
1.11655 
1.14689 
1.17654 
1.20548 
1.2337 
1.26116 
1.28786 
1.31377 
1.33887 
0.277557 
0.317591 
0.357595 
0.397538 
0.437389 
0.477119 
0.516697 
0.556092 
0.595276 
0.634218 
0.672889 
0.71126 
0.749302 
0.786986 
0.824284 
0.861168 
0.897611 
0.933587 
0.969067 
1.00403 
1.03844 
1.07228 
1.10553 
1.13815 
1.17014 
1.20145 
1.23208 
1.26201 
1.2912 
1.31964 
1.34731 
1.3742 
1.40028 
0.307439 
0.34845 
0.38943 
0.430349 
0.471177 
0.511884 
0.552438 
0.59281 
0.63297 
0.672889 
0.712537 
0.751884 
0.790903 
0.829563 
0.867838 
0.905699 
0.943119 
0.98007 
1.01653 
1.05246 
1.08785 
1.12267 
1.15689 
1.1905 
1.22346 
1.25575 
1.28736 
1.31825 
1.34842 
1.37784 
1.40649 
1.43435 
1.46141 
0.33702 
0.379008 
0.420965 
0.462861 
0.504665 
0.546348 
0.587879 
0.629228 
0.670365 
0.71126 
0.751884 
0.792208 
0.832203 
0.87184 
0.911092 
0.949929 
0.988325 
1.02625 
1.06369 
1.1006 
1.13697 
1.17276 
1.20796 
1.24254 
1.27648 
1.30975 
1.34233 
1.3742 
1.40535 
1.43574 
1.46537 
1.49421 
1.52224 
0.366273 
0.409237 
0.45217 
0.495043 
0.537824 
0.580484 
0.622991 
0.665316 
0.70743 
0.749302 
0.790903 
0.832203 
0.873174 
0.913788 
0.954016 
0.99383 
1.0332 
1.07211 
1.11052 
1.14841 
1.18575 
1.22252 
1.2587 
1.29425 
1.32917 
1.36341 
1.39697 
1.42982 
1.46194 
1.49332 
1.52392 
1.55373 
1.58274 
0.395167 
0.439108 
0.483018 
0.526868 
0.570625 
0.614261 
0.657745 
0.701047 
0.744137 
0.786986 
0.829563 
0.87184 
0.913788 
0.955379 
0.996583 
1.03737 
1.07772 
1.1176 
1.15699 
1.19586 
1.23418 
1.27192 
1.30908 
1.34561 
1.3815 
1.41672 
1.45126 
1.48509 
1.51818 
1.55053 
1.58211 
1.6129 
1.64289 
0.423676 
0.468594 
0.51348 
0.558306 
0.603041 
0.647653 
0.692114 
0.736392 
0.780459 
0.824284 
0.867838 
0.911092 
0.954016 
0.996583 
1.03876 
1.08053 
1.12186 
1.16272 
1.20308 
1.24292 
1.28222 
1.32094 
1.35907 
1.39658 
1.43344 
1.46964 
1.50516 
1.53996 
1.57404 
1.60736 
1.63992 
1.67168 
1.70265 
0.451771 
0.497665 
0.543529 
0.589331 
0.635042 
0.680631 
0.726068 
0.771324 
0.816367 
0.861168 
0.905699 
0.949929 
0.99383 
1.03737 
1.08053 
1.12327 
1.16558 
1.20741 
1.24875 
1.28957 
1.32984 
1.36954 
1.40865 
1.44713 
1.48498 
1.52215 
1.55864 
1.59442 
1.62947 
1.66378 
1.69731 
1.73005 
1.76199 
0.479426 
0.526296 
0.573136 
0.619915 
0.666602 
0.713168 
0.759582 
0.805814 
0.851833 
0.897611 
0.943119 
0.988325 
1.0332 
1.07772 
1.12186 
1.16558 
1.20886 
1.25167 
1.29398 
1.33578 
1.37703 
1.41771 
1.45779 
1.49725 
1.53607 
1.57422 
1.61169 
1.64845 
1.68447 
1.71975 
1.75426 
1.78798 
1.8209 
0.506611 
0.554459 
0.602275 
0.650031 
0.697695 
0.745237 
0.792627 
0.839836 
0.886832 
0.933587 
0.98007 
1.02625 
1.07211 
1.1176 
1.16272 
1.20741 
1.25167 
1.29546 
1.33875 
1.38152 
1.42375 
1.4654 
1.50646 
1.5469 
1.58669 
1.62582 
1.66426 
1.702 
1.739 
1.77526 
1.81074 
1.84544 
1.87933 
0.533303 
0.582126 
0.630919 
0.679652 
0.728292 
0.776811 
0.825178 
0.873363 
0.921336 
0.969067 
1.01653 
1.06369 
1.11052 
1.15699 
1.20308 
1.24875 
1.29398 
1.33875 
1.38302 
1.42677 
1.46997 
1.5126 
1.55463 
1.59605 
1.63682 
1.67693 
1.71635 
1.75506 
1.79304 
1.83027 
1.86673 
1.9024 
1.93727 
0.559473 
0.609273 
0.659043 
0.708752 
0.758369 
0.807864 
0.857208 
0.906369 
0.955319 
1.00403 
1.05246 
1.1006 
1.14841 
1.19586 
1.24292 
1.28957 
1.33578 
1.38152 
1.42677 
1.47149 
1.51567 
1.55928 
1.60229 
1.64468 
1.68643 
1.72751 
1.76791 
1.80759 
1.84655 
1.88476 
1.9222 
1.95885 
1.99469 
0.585097 
0.635874 
0.68662 
0.737306 
0.787899 
0.838371 
0.888691 
0.938829 
0.988755 
1.03844 
1.08785 
1.13697 
1.18575 
1.23418 
1.28222 
1.32984 
1.37703 
1.42375 
1.46997 
1.51567 
1.56083 
1.60541 
1.6494 
1.69277 
1.73549 
1.77755 
1.81892 
1.85959 
1.89952 
1.9387 
1.97712 
2.01475 
2.05157 
0.61015 
0.661903 
0.713626 
0.765288 
0.816858 
0.868307 
0.919603 
0.970718 
1.02162 
1.07228 
1.12267 
1.17276 
1.22252 
1.27192 
1.32094 
1.36954 
1.41771 
1.4654 
1.5126 
1.55928 
1.60541 
1.65097 
1.69593 
1.74028 
1.78398 
1.82702 
1.86937 
1.91101 
1.95192 
1.99208 
2.03147 
2.07007 
2.10787 
0.634607 
0.687337 
0.740036 
0.792675 
0.845221 
0.897647 
0.94992 
1.00201 
1.05389 
1.10553 
1.15689 
1.20796 
1.2587 
1.30908 
1.35907 
1.40865 
1.45779 
1.50646 
1.55463 
1.60229 
1.6494 
1.69593 
1.74188 
1.7872 
1.83188 
1.87589 
1.91921 
1.96183 
2.00372 
2.04485 
2.08522 
2.1248 
2.16358 
0.658444 
0.712151 
0.765827 
0.819442 
0.872965 
0.926367 
0.979616 
1.03268 
1.08554 
1.13815 
1.1905 
1.24254 
1.29425 
1.34561 
1.39658 
1.44713 
1.49725 
1.5469 
1.59605 
1.64468 
1.69277 
1.74028 
1.7872 
1.8335 
1.87915 
1.92414 
1.96844 
2.01203 
2.0549 
2.09701 
2.13836 
2.17891 
2.21867 
0.681639 
0.736322 
0.790974 
0.845566 
0.900066 
0.954444 
1.00867 
1.06271 
1.11655 
1.17014 
1.22346 
1.27648 
1.32917 
1.3815 
1.43344 
1.48498 
1.53607 
1.58669 
1.63682 
1.68643 
1.73549 
1.78398 
1.83188 
1.87915 
1.92578 
1.97175 
2.01703 
2.0616 
2.10544 
2.14853 
2.19085 
2.23238 
2.27311 
0.704168 
0.759827 
0.815456 
0.871024 
0.9265 
0.981855 
1.03706 
1.09208 
1.14689 
1.20145 
1.25575 
1.30975 
1.36341 
1.41672 
1.46964 
1.52215 
1.57422 
1.62582 
1.67693 
1.72751 
1.77755 
1.82702 
1.87589 
1.92414 
1.97175 
2.01869 
2.06495 
2.11049 
2.15531 
2.19937 
2.24267 
2.28518 
2.32689 
0.726009 
0.782645 
0.83925 
0.895795 
0.952248 
1.00858 
1.06476 
1.12076 
1.17654 
1.23208 
1.28736 
1.34233 
1.39697 
1.45126 
1.50516 
1.55864 
1.61169 
1.66426 
1.71635 
1.76791 
1.81892 
1.86937 
1.91921 
1.96844 
2.01703 
2.06495 
2.11218 
2.1587 
2.20449 
2.24954 
2.29381 
2.3373 
2.37998 
0.747141 
0.804753 
0.862335 
0.919856 
0.977286 
1.03459 
1.09175 
1.14872 
1.20548 
1.26201 
1.31825 
1.3742 
1.42982 
1.48509 
1.53996 
1.59442 
1.64845 
1.702 
1.75506 
1.80759 
1.85959 
1.91101 
1.96183 
2.01203 
2.0616 
2.11049 
2.1587 
2.2062 
2.25297 
2.29899 
2.34424 
2.3887 
2.43236 
0.767544 
0.826133 
0.884691 
0.943189 
1.00159 
1.05988 
1.11801 
1.17596 
1.2337 
1.2912 
1.34842 
1.40535 
1.46194 
1.51818 
1.57404 
1.62947 
1.68447 
1.739 
1.79304 
1.84655 
1.89952 
1.95192 
2.00372 
2.0549 
2.10544 
2.15531 
2.20449 
2.25297 
2.30071 
2.34771 
2.39394 
2.43938 
2.48401 
0.787197 
0.846762 
0.906297 
0.965771 
1.02515 
1.08441 
1.14352 
1.20245 
1.26116 
1.31964 
1.37784 
1.43574 
1.49332 
1.55053 
1.60736 
1.66378 
1.71975 
1.77526 
1.83027 
1.88476 
1.9387 
1.99208 
2.04485 
2.09701 
2.14853 
2.19937 
2.24954 
2.29899 
2.34771 
2.39568 
2.44289 
2.48931 
2.53492 
0.806081 
0.866623 
0.927135 
0.987585 
1.04794 
1.10818 
1.16827 
1.22817 
1.28786 
1.34731 
1.40649 
1.46537 
1.52392 
1.58211 
1.63992 
1.69731 
1.75426 
1.81074 
1.86673 
1.9222 
1.97712 
2.03147 
2.08522 
2.13836 
2.19085 
2.24267 
2.29381 
2.34424 
2.39394 
2.44289 
2.49107 
2.53846 
2.58505 
0.824178 
0.885697 
0.947185 
1.00861 
1.06995 
1.13116 
1.19222 
1.2531 
1.31377 
1.3742 
1.43435 
1.49421 
1.55373 
1.6129 
1.67168 
1.73005 
1.78798 
1.84544 
1.9024 
1.95885 
2.01475 
2.07007 
2.1248 
2.17891 
2.23238 
2.28518 
2.3373 
2.3887 
2.43938 
2.48931 
2.53846 
2.58683 
2.6344 
0.841471 
0.903966 
0.96643 
1.02883 
1.09115 
1.15334 
1.21537 
1.27723 
1.33887 
1.40028 
1.46141 
1.52224 
1.58274 
1.64289 
1.70265 
1.76199 
1.8209 
1.87933 
1.93727 
1.99469 
2.05157 
2.10787 
2.16358 
2.21867 
2.27311 
2.32689 
2.37998 
2.43236 
2.48401 
2.53492 
2.58505 
2.6344 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.66096
-4.86545
-8.01058
-11.0539
-14.0386
-16.9946
-19.9578
-22.9241
-25.892
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd7.png');
clf
figure(2);
saveas(gcf,'oneResidualInd7.png');

N = [
4
8
16
32
];
E = [
-11.4988
-13.4521
-15.3979
-17.3979
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2e-05
0.000126
0.006808
0.367401
];
T2 = [
0.000684
0.00787
0.103687
1.27871
];
figure(4);
subplot(3,1,1);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0 
0.243018 
0.47351 
0.674499 
0.831545 
0.243772 
0.55405 
0.84828 
1.11267 
1.33507 
0.476524 
0.850205 
1.20746 
1.53476 
1.82021 
0.68195 
1.11736 
1.53668 
1.92612 
2.27354 
0.84896 
1.34253 
1.82322 
2.27429 
2.68137 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.521655
0.0981642
-0.193969
-0.450156
-0.696768
-0.940756
-1.184
-1.42703
-1.67
-1.91295
-2.15589
-2.39883
-2.64177
-2.88471
-3.12764
-3.37058
-3.61352
-3.85646
-4.0994
-4.34234
-4.58528
-4.82822
-5.07116
-5.31409
-5.55703
-5.79997
-6.04291
-6.28585
-6.52879
-6.77173
-7.01467
-7.25761
-7.50055
-7.74348
-7.98642
-8.22936
-8.4723
-8.71524
-8.95818
-9.20112
-9.44406
-9.687
-9.92993
-10.1729
-10.4158
-10.6588
-10.9017
-11.1446
-11.3876
-11.6305
-11.8734
-12.1164
-12.3593
-12.6023
-12.8452
-13.0881
-13.3311
-13.574
-13.817
-14.0599
-14.3028
-14.5458
-14.7887
-15.0317
-15.2746
-15.5175
-15.7605
-16.0034
-16.2463
-16.4893
-16.7322
-16.9752
-17.2181
-17.461
-17.704
-17.9469
-18.1899
-18.4328
-18.6757
-18.9187
-19.1616
-19.4046
-19.6475
-19.8904
-20.1334
-20.3763
-20.6192
-20.8622
-21.1051
-21.3481
-21.591
-21.8339
-22.0769
-22.3198
-22.5628
-22.8057
-23.0486
-23.2916
-23.5345
-23.7775
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
0 
0.123642 
0.246052 
0.364827 
0.47797 
0.58366 
0.680212 
0.766063 
0.839705 
0.123663 
0.263909 
0.402186 
0.536657 
0.665451 
0.786783 
0.898987 
1.00055 
1.09014 
0.246137 
0.402249 
0.556313 
0.706492 
0.850956 
0.987944 
1.11581 
1.23305 
1.33835 
0.36502 
0.536825 
0.706593 
0.872454 
1.03258 
1.18522 
1.32874 
1.46163 
1.58259 
0.478318 
0.665768 
0.851191 
1.0327 
1.20848 
1.37676 
1.53591 
1.68444 
1.82103 
0.584226 
0.787297 
0.988344 
1.18548 
1.37688 
1.56079 
1.73556 
1.89972 
2.05192 
0.681101 
0.899762 
1.1164 
1.32914 
1.53615 
1.73567 
1.92605 
2.1058 
2.27361 
0.767504 
1.00165 
1.23382 
1.46215 
1.68476 
1.89988 
2.10587 
2.30119 
2.48454 
0.842364 
1.09158 
1.33924 
1.58315 
1.82137 
2.05211 
2.2737 
2.48456 
2.68321 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.690877
0.280272
0.00391975
-0.208962
-0.393778
-0.56651
-0.734066
-0.899397
-1.06376
-1.22771
-1.39147
-1.55516
-1.7188
-1.88243
-2.04605
-2.20967
-2.37329
-2.53691
-2.70053
-2.86414
-3.02776
-3.19138
-3.35499
-3.51861
-3.68222
-3.84584
-4.00946
-4.17307
-4.33669
-4.50031
-4.66392
-4.82754
-4.99116
-5.15477
-5.31839
-5.48201
-5.64562
-5.80924
-5.97286
-6.13647
-6.30009
-6.46371
-6.62732
-6.79094
-6.95456
-7.11817
-7.28179
-7.44541
-7.60902
-7.77264
-7.93626
-8.09987
-8.26349
-8.42711
-8.59072
-8.75434
-8.91796
-9.08157
-9.24519
-9.40881
-9.57242
-9.73604
-9.89966
-10.0633
-10.2269
-10.3905
-10.5541
-10.7177
-10.8814
-11.045
-11.2086
-11.3722
-11.5358
-11.6994
-11.8631
-12.0267
-12.1903
-12.3539
-12.5175
-12.6811
-12.8448
-13.0084
-13.172
-13.3356
-13.4992
-13.6628
-13.8265
-13.9901
-14.1537
-14.3173
-14.4809
-14.6445
-14.8082
-14.9718
-15.1354
-15.299
-15.4626
-15.6262
-15.7899
-15.9535
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
0 
0.0620297 
0.124073 
0.185717 
0.246671 
0.306678 
0.365496 
0.422892 
0.478639 
0.532517 
0.584316 
0.633831 
0.680869 
0.725245 
0.766783 
0.805316 
0.840672 
0.0620303 
0.128308 
0.194343 
0.259918 
0.324786 
0.388703 
0.45143 
0.512733 
0.572387 
0.630172 
0.685877 
0.7393 
0.790244 
0.838528 
0.883975 
0.926423 
0.965726 
0.124076 
0.194345 
0.264343 
0.333854 
0.402644 
0.470476 
0.537113 
0.602326 
0.665888 
0.727581 
0.787193 
0.844523 
0.899375 
0.951567 
1.00092 
1.04729 
1.0905 
0.185723 
0.259923 
0.333857 
0.407296 
0.480007 
0.551755 
0.622305 
0.691428 
0.758899 
0.8245 
0.88802 
0.949258 
1.00802 
1.06412 
1.11738 
1.16766 
1.21478 
0.246681 
0.324796 
0.402652 
0.480012 
0.556641 
0.632303 
0.706765 
0.779798 
0.851179 
0.920689 
0.988118 
1.05326 
1.11593 
1.17594 
1.23311 
1.28729 
1.33833 
0.306694 
0.388719 
0.470489 
0.551765 
0.632308 
0.711883 
0.790257 
0.867201 
0.942491 
1.01591 
1.08725 
1.1563 
1.22288 
1.28679 
1.34787 
1.40596 
1.4609 
0.365519 
0.451452 
0.537134 
0.622322 
0.706777 
0.790264 
0.872548 
0.953402 
1.0326 
1.10993 
1.18517 
1.25813 
1.32862 
1.39644 
1.46143 
1.52342 
1.58227 
0.422924 
0.512764 
0.602354 
0.691452 
0.779818 
0.867215 
0.953409 
1.03817 
1.12128 
1.20252 
1.28167 
1.35854 
1.43293 
1.50466 
1.57355 
1.63946 
1.70221 
0.478681 
0.572428 
0.665926 
0.758933 
0.851208 
0.942513 
1.03262 
1.12129 
1.2083 
1.29345 
1.37651 
1.45728 
1.53558 
1.61122 
1.68402 
1.75383 
1.82049 
0.532571 
0.630225 
0.72763 
0.824545 
0.920727 
1.01594 
1.10995 
1.20253 
1.29345 
1.3825 
1.46947 
1.55416 
1.63636 
1.71591 
1.79261 
1.86633 
1.9369 
0.584384 
0.685944 
0.787256 
0.888077 
0.988166 
1.08729 
1.18521 
1.28169 
1.37652 
1.46948 
1.56035 
1.64894 
1.73506 
1.81851 
1.89912 
1.97674 
2.05122 
0.633916 
0.739383 
0.8446 
0.949327 
1.05332 
1.15635 
1.25818 
1.35857 
1.45731 
1.55417 
1.64895 
1.74145 
1.83147 
1.91882 
2.00334 
2.08487 
2.16325 
0.680976 
0.790348 
0.89947 
1.0081 
1.116 
1.22294 
1.32867 
1.43297 
1.53561 
1.63638 
1.73507 
1.83147 
1.92539 
2.01666 
2.10508 
2.19051 
2.2728 
0.72538 
0.838656 
0.951682 
1.06422 
1.17602 
1.28686 
1.3965 
1.5047 
1.61125 
1.71593 
1.81852 
1.91883 
2.01666 
2.11183 
2.20416 
2.2935 
2.37969 
0.766958 
0.884136 
1.00106 
1.1175 
1.23321 
1.34795 
1.46149 
1.5736 
1.68406 
1.79264 
1.89914 
2.00336 
2.10509 
2.20416 
2.3004 
2.39364 
2.48373 
0.805558 
0.926625 
1.04745 
1.16778 
1.2874 
1.40604 
1.52349 
1.63951 
1.75387 
1.86636 
1.97676 
2.08488 
2.19052 
2.2935 
2.39364 
2.49078 
2.58477 
0.841065 
0.965968 
1.09068 
1.21492 
1.33843 
1.46099 
1.58234 
1.70226 
1.82053 
1.93693 
2.05124 
2.16326 
2.27281 
2.37969 
2.48373 
2.58477 
2.68263 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.839856
0.445485
0.162831
-0.0480124
-0.216335
-0.360707
-0.491939
-0.616047
-0.73631
-0.854496
-0.971557
-1.08801
-1.20412
-1.32006
-1.4359
-1.55168
-1.66743
-1.78317
-1.89889
-2.01462
-2.13033
-2.24605
-2.36177
-2.47748
-2.5932
-2.70891
-2.82463
-2.94034
-3.05606
-3.17177
-3.28749
-3.4032
-3.51892
-3.63463
-3.75035
-3.86606
-3.98178
-4.09749
-4.21321
-4.32892
-4.44464
-4.56035
-4.67607
-4.79179
-4.9075
-5.02322
-5.13893
-5.25465
-5.37036
-5.48608
-5.60179
-5.71751
-5.83322
-5.94894
-6.06465
-6.18037
-6.29608
-6.4118
-6.52751
-6.64323
-6.75894
-6.87466
-6.99037
-7.10609
-7.2218
-7.33752
-7.45323
-7.56895
-7.68466
-7.80038
-7.91609
-8.03181
-8.14752
-8.26324
-8.37895
-8.49467
-8.61038
-8.7261
-8.84181
-8.95753
-9.07324
-9.18896
-9.30467
-9.42039
-9.5361
-9.65182
-9.76753
-9.88325
-9.99896
-10.1147
-10.2304
-10.3461
-10.4618
-10.5775
-10.6933
-10.809
-10.9247
-11.0404
-11.1561
-11.2718
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
0 
0.0302511 
0.0610235 
0.0919242 
0.122816 
0.153629 
0.184318 
0.214842 
0.245169 
0.275263 
0.305095 
0.334632 
0.363846 
0.392706 
0.421184 
0.449252 
0.476881 
0.504045 
0.530716 
0.556868 
0.582476 
0.607515 
0.631959 
0.655785 
0.678969 
0.701489 
0.723322 
0.744448 
0.764846 
0.784495 
0.803376 
0.82147 
0.838757 
0.0302511 
0.0622064 
0.0941362 
0.126066 
0.157952 
0.18975 
0.22142 
0.252923 
0.284227 
0.315299 
0.346108 
0.376623 
0.406813 
0.43665 
0.466105 
0.49515 
0.523756 
0.551896 
0.579544 
0.606673 
0.633257 
0.659272 
0.684693 
0.709496 
0.733656 
0.757153 
0.779963 
0.802066 
0.82344 
0.844065 
0.863923 
0.882995 
0.901264 
0.0610235 
0.0941362 
0.127165 
0.160134 
0.19303 
0.225822 
0.258477 
0.290964 
0.323248 
0.3553 
0.387087 
0.418579 
0.449747 
0.480562 
0.510994 
0.541015 
0.570598 
0.599716 
0.62834 
0.656446 
0.684008 
0.710999 
0.737397 
0.763176 
0.788313 
0.812787 
0.836573 
0.859653 
0.882003 
0.903606 
0.924441 
0.94449 
0.963737 
0.0919242 
0.126066 
0.160134 
0.194127 
0.22803 
0.261818 
0.295463 
0.328934 
0.362201 
0.395233 
0.428 
0.460471 
0.492618 
0.52441 
0.55582 
0.586819 
0.617379 
0.647473 
0.677075 
0.706158 
0.734696 
0.762664 
0.790039 
0.816795 
0.842909 
0.868359 
0.893122 
0.917178 
0.940506 
0.963085 
0.984897 
1.00592 
1.02615 
0.122816 
0.157953 
0.19303 
0.22803 
0.262934 
0.297716 
0.332351 
0.366808 
0.401058 
0.435071 
0.468818 
0.502269 
0.535394 
0.568165 
0.600552 
0.632529 
0.664066 
0.695138 
0.725717 
0.755777 
0.785292 
0.814238 
0.842589 
0.870321 
0.897412 
0.923839 
0.949579 
0.974612 
0.998916 
1.02247 
1.04526 
1.06726 
1.08846 
0.153629 
0.189751 
0.225822 
0.261818 
0.297716 
0.33349 
0.369113 
0.404555 
0.439789 
0.474784 
0.509512 
0.543942 
0.578046 
0.611795 
0.645161 
0.678116 
0.710631 
0.74268 
0.774236 
0.805273 
0.835766 
0.865688 
0.895016 
0.923726 
0.951794 
0.979197 
1.00591 
1.03192 
1.0572 
1.08174 
1.1055 
1.12848 
1.15066 
0.184318 
0.22142 
0.258477 
0.295463 
0.332351 
0.369113 
0.405721 
0.442149 
0.478365 
0.514342 
0.55005 
0.585461 
0.620544 
0.655272 
0.689616 
0.723549 
0.757042 
0.790069 
0.822602 
0.854617 
0.886086 
0.916986 
0.947291 
0.976977 
1.00602 
1.0344 
1.0621 
1.08908 
1.11534 
1.14085 
1.16559 
1.18955 
1.2127 
0.214843 
0.252923 
0.290964 
0.328935 
0.366808 
0.404555 
0.442149 
0.479559 
0.516758 
0.553717 
0.590406 
0.626796 
0.662859 
0.698566 
0.733888 
0.768799 
0.80327 
0.837274 
0.870785 
0.903777 
0.936224 
0.968101 
0.999383 
1.03005 
1.06007 
1.08943 
1.1181 
1.14606 
1.17329 
1.19978 
1.2255 
1.25043 
1.27456 
0.245169 
0.284228 
0.323249 
0.362202 
0.401058 
0.439789 
0.478365 
0.516758 
0.554939 
0.592879 
0.630548 
0.667918 
0.70496 
0.741646 
0.777947 
0.813836 
0.849285 
0.884267 
0.918756 
0.952725 
0.986149 
1.019 
1.05126 
1.0829 
1.1139 
1.14424 
1.17388 
1.20282 
1.23103 
1.2585 
1.28519 
1.3111 
1.33621 
0.275264 
0.3153 
0.3553 
0.395234 
0.435072 
0.474784 
0.514343 
0.553717 
0.592879 
0.631799 
0.670448 
0.708798 
0.746819 
0.784483 
0.821763 
0.85863 
0.895057 
0.931017 
0.966483 
1.00143 
1.03583 
1.06966 
1.1029 
1.13552 
1.16749 
1.1988 
1.22943 
1.25934 
1.28853 
1.31697 
1.34465 
1.37153 
1.39762 
0.305095 
0.346109 
0.387087 
0.428001 
0.468819 
0.509512 
0.550051 
0.590406 
0.630548 
0.670448 
0.710077 
0.749406 
0.788406 
0.82705 
0.865308 
0.903153 
0.940558 
0.977496 
1.01394 
1.04986 
1.08524 
1.12005 
1.15426 
1.18786 
1.22081 
1.2531 
1.2847 
1.3156 
1.34576 
1.37518 
1.40383 
1.43169 
1.45875 
0.334633 
0.376623 
0.41858 
0.460472 
0.50227 
0.543943 
0.585461 
0.626796 
0.667918 
0.708798 
0.749406 
0.789714 
0.829693 
0.869315 
0.908552 
0.947375 
0.985758 
1.02367 
1.06109 
1.098 
1.13435 
1.17014 
1.20533 
1.2399 
1.27383 
1.3071 
1.33967 
1.37154 
1.40269 
1.43308 
1.46271 
1.49155 
1.51958 
0.363847 
0.406814 
0.449748 
0.492619 
0.535395 
0.578047 
0.620545 
0.662859 
0.704961 
0.746819 
0.788407 
0.829693 
0.870651 
0.911251 
0.951466 
0.991268 
1.03063 
1.06952 
1.10792 
1.1458 
1.18313 
1.2199 
1.25606 
1.29161 
1.32652 
1.36076 
1.39432 
1.42716 
1.45928 
1.49065 
1.52126 
1.55107 
1.58009 
0.392707 
0.436651 
0.480563 
0.524411 
0.568166 
0.611796 
0.655273 
0.698566 
0.741646 
0.784484 
0.82705 
0.869315 
0.911252 
0.95283 
0.994023 
1.0348 
1.07514 
1.11501 
1.15439 
1.19325 
1.23156 
1.2693 
1.30644 
1.34297 
1.37885 
1.41407 
1.4486 
1.48243 
1.51552 
1.54787 
1.57945 
1.61024 
1.64023 
0.421186 
0.466107 
0.510995 
0.555821 
0.600554 
0.645162 
0.689618 
0.733889 
0.777948 
0.821764 
0.865308 
0.908552 
0.951466 
0.994023 
1.03619 
1.07795 
1.11927 
1.16012 
1.20047 
1.2403 
1.27959 
1.31831 
1.35643 
1.39394 
1.4308 
1.46699 
1.5025 
1.5373 
1.57137 
1.6047 
1.63725 
1.66902 
1.69999 
0.449254 
0.495151 
0.541017 
0.58682 
0.63253 
0.678117 
0.72355 
0.7688 
0.813837 
0.858631 
0.903154 
0.947376 
0.991268 
1.0348 
1.07795 
1.12069 
1.16298 
1.20481 
1.24614 
1.28695 
1.32721 
1.36691 
1.40601 
1.44449 
1.48233 
1.5195 
1.55599 
1.59176 
1.62681 
1.66111 
1.69464 
1.72739 
1.75933 
0.476883 
0.523758 
0.570601 
0.617381 
0.664068 
0.710633 
0.757044 
0.803271 
0.849286 
0.895059 
0.940559 
0.985759 
1.03063 
1.07514 
1.11927 
1.16298 
1.20625 
1.24906 
1.29136 
1.33315 
1.3744 
1.41507 
1.45514 
1.4946 
1.53342 
1.57157 
1.60903 
1.64578 
1.68181 
1.71709 
1.75159 
1.78532 
1.81824 
0.504047 
0.551898 
0.599718 
0.647476 
0.69514 
0.742682 
0.790071 
0.837276 
0.884269 
0.931019 
0.977497 
1.02367 
1.06952 
1.11501 
1.16012 
1.20481 
1.24906 
1.29284 
1.33612 
1.37889 
1.42111 
1.46276 
1.50381 
1.54425 
1.58404 
1.62316 
1.6616 
1.69933 
1.73634 
1.77259 
1.80808 
1.84278 
1.87667 
0.530719 
0.579547 
0.628343 
0.677078 
0.72572 
0.774239 
0.822605 
0.870788 
0.918758 
0.966485 
1.01394 
1.0611 
1.10792 
1.15439 
1.20047 
1.24614 
1.29137 
1.33612 
1.38039 
1.42413 
1.46733 
1.50995 
1.55198 
1.5934 
1.63416 
1.67427 
1.71368 
1.75239 
1.79037 
1.8276 
1.86406 
1.89974 
1.93461 
0.556872 
0.606676 
0.65645 
0.706161 
0.75578 
0.805276 
0.85462 
0.90378 
0.952727 
1.00143 
1.04987 
1.098 
1.1458 
1.19325 
1.24031 
1.28695 
1.33315 
1.37889 
1.42413 
1.46885 
1.51302 
1.55663 
1.59964 
1.64202 
1.68377 
1.72485 
1.76524 
1.80493 
1.84388 
1.88209 
1.91953 
1.95618 
1.99203 
0.582481 
0.633262 
0.684012 
0.7347 
0.785296 
0.835769 
0.88609 
0.936227 
0.986152 
1.03583 
1.08524 
1.13435 
1.18314 
1.23156 
1.27959 
1.32722 
1.3744 
1.42111 
1.46733 
1.51303 
1.55818 
1.60276 
1.64674 
1.69011 
1.73283 
1.77489 
1.81626 
1.85692 
1.89685 
1.93603 
1.97445 
2.01208 
2.0489 
0.60752 
0.659277 
0.711004 
0.762669 
0.814242 
0.865692 
0.91699 
0.968104 
1.01901 
1.06967 
1.12005 
1.17014 
1.2199 
1.2693 
1.31831 
1.36691 
1.41507 
1.46276 
1.50995 
1.55663 
1.60276 
1.64831 
1.69327 
1.73762 
1.78132 
1.82435 
1.8667 
1.90834 
1.94924 
1.9894 
2.0288 
2.0674 
2.10521 
0.631964 
0.684699 
0.737402 
0.790044 
0.842594 
0.895021 
0.947295 
0.999387 
1.05127 
1.1029 
1.15427 
1.20533 
1.25607 
1.30644 
1.35643 
1.40601 
1.45515 
1.50381 
1.55198 
1.59964 
1.64674 
1.69327 
1.73921 
1.78453 
1.82921 
1.87322 
1.91654 
1.95916 
2.00104 
2.04218 
2.08255 
2.12213 
2.16091 
0.655791 
0.709502 
0.763182 
0.816801 
0.870327 
0.923731 
0.976982 
1.03005 
1.08291 
1.13552 
1.18786 
1.2399 
1.29162 
1.34297 
1.39394 
1.44449 
1.4946 
1.54425 
1.5934 
1.64202 
1.69011 
1.73762 
1.78453 
1.83083 
1.87648 
1.92147 
1.96577 
2.00936 
2.05222 
2.09434 
2.13568 
2.17624 
2.216 
0.678977 
0.733664 
0.788321 
0.842916 
0.897419 
0.9518 
1.00603 
1.06007 
1.11391 
1.1675 
1.22082 
1.27383 
1.32652 
1.37885 
1.4308 
1.48233 
1.53342 
1.58404 
1.63416 
1.68377 
1.73283 
1.78132 
1.82921 
1.87648 
1.92311 
1.96907 
2.01435 
2.05892 
2.10276 
2.14585 
2.18817 
2.22971 
2.27044 
0.701498 
0.757162 
0.812795 
0.868367 
0.923847 
0.979204 
1.03441 
1.08943 
1.14424 
1.19881 
1.2531 
1.3071 
1.36077 
1.41407 
1.46699 
1.5195 
1.57157 
1.62317 
1.67427 
1.72485 
1.77489 
1.82435 
1.87322 
1.92147 
1.96907 
2.01602 
2.06227 
2.10781 
2.15263 
2.1967 
2.24 
2.28251 
2.32422 
0.723333 
0.779974 
0.836584 
0.893132 
0.949588 
1.00592 
1.0621 
1.1181 
1.17389 
1.22943 
1.28471 
1.33968 
1.39432 
1.44861 
1.5025 
1.55599 
1.60903 
1.66161 
1.71368 
1.76524 
1.81626 
1.8667 
1.91654 
1.96577 
2.01435 
2.06227 
2.1095 
2.15602 
2.20181 
2.24686 
2.29113 
2.33462 
2.37731 
0.744461 
0.802078 
0.859664 
0.917189 
0.974622 
1.03193 
1.08909 
1.14607 
1.20283 
1.25935 
1.3156 
1.37155 
1.42717 
1.48243 
1.5373 
1.59177 
1.64579 
1.69934 
1.75239 
1.80493 
1.85692 
1.90834 
1.95916 
2.00936 
2.05892 
2.10781 
2.15602 
2.20352 
2.25029 
2.29631 
2.34156 
2.38602 
2.42969 
0.764861 
0.823455 
0.882017 
0.940518 
0.998928 
1.05721 
1.11535 
1.1733 
1.23104 
1.28854 
1.34577 
1.40269 
1.45929 
1.51552 
1.57138 
1.62681 
1.68181 
1.73634 
1.79037 
1.84388 
1.89685 
1.94924 
2.00104 
2.05222 
2.10276 
2.15263 
2.20181 
2.25029 
2.29803 
2.34503 
2.39126 
2.4367 
2.48134 
0.784513 
0.844083 
0.903622 
0.9631 
1.02249 
1.08175 
1.14086 
1.19979 
1.2585 
1.31698 
1.37518 
1.43308 
1.49066 
1.54787 
1.6047 
1.66111 
1.71709 
1.77259 
1.8276 
1.88209 
1.93603 
1.98941 
2.04218 
2.09434 
2.14585 
2.1967 
2.24686 
2.29631 
2.34503 
2.393 
2.44021 
2.48663 
2.53224 
0.803399 
0.863945 
0.92446 
0.984913 
1.04528 
1.10552 
1.1656 
1.22551 
1.2852 
1.34465 
1.40383 
1.46271 
1.52126 
1.57945 
1.63726 
1.69465 
1.7516 
1.80808 
1.86406 
1.91953 
1.97445 
2.0288 
2.08255 
2.13568 
2.18817 
2.24 
2.29113 
2.34156 
2.39126 
2.44021 
2.48839 
2.53578 
2.58237 
0.821502 
0.883022 
0.944512 
1.00594 
1.06728 
1.1285 
1.18956 
1.25044 
1.31111 
1.37154 
1.43169 
1.49155 
1.55108 
1.61024 
1.66903 
1.72739 
1.78532 
1.84278 
1.89974 
1.95618 
2.01208 
2.0674 
2.12213 
2.17624 
2.22971 
2.28251 
2.33462 
2.38603 
2.4367 
2.48663 
2.53578 
2.58415 
2.63172 
0.838807 
0.901296 
0.96376 
1.02617 
1.08848 
1.15067 
1.21271 
1.27457 
1.33622 
1.39762 
1.45875 
1.51959 
1.58009 
1.64023 
1.69999 
1.75934 
1.81824 
1.87667 
1.93461 
1.99203 
2.04891 
2.10521 
2.16091 
2.216 
2.27044 
2.32422 
2.37731 
2.42969 
2.48134 
2.53224 
2.58237 
2.63172 
2.68026 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
0.952661
0.58154
0.292744
0.0699217
-0.105363
-0.248518
-0.370801
-0.479844
-0.580603
-0.676211
-0.768626
-0.859062
-0.94827
-1.03671
-1.12468
-1.21235
-1.29984
-1.38721
-1.4745
-1.56175
-1.64897
-1.73618
-1.82337
-1.91055
-1.99773
-2.0849
-2.17208
-2.25925
-2.34642
-2.43359
-2.52076
-2.60793
-2.6951
-2.78227
-2.86945
-2.95662
-3.04379
-3.13096
-3.21813
-3.3053
-3.39247
-3.47964
-3.56681
-3.65398
-3.74115
-3.82832
-3.91549
-4.00266
-4.08983
-4.177
-4.26417
-4.35134
-4.43851
-4.52568
-4.61285
-4.70002
-4.78719
-4.87436
-4.96154
-5.04871
-5.13588
-5.22305
-5.31022
-5.39739
-5.48456
-5.57173
-5.6589
-5.74607
-5.83324
-5.92041
-6.00758
-6.09475
-6.18192
-6.26909
-6.35626
-6.44343
-6.5306
-6.61777
-6.70494
-6.79211
-6.87928
-6.96645
-7.05363
-7.1408
-7.22797
-7.31514
-7.40231
-7.48948
-7.57665
-7.66382
-7.75099
-7.83816
-7.92533
-8.0125
-8.09967
-8.18684
-8.27401
-8.36118
-8.44835
-8.53552
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd8.png');
clf
figure(2);
saveas(gcf,'oneResidualInd8.png');

N = [
4
8
16
32
];
E = [
-6.65464
-9.14527
-10.2898
-8.52531
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.1e-05
0.000211
0.00647
0.357137
];
T2 = [
0.009879
0.086642
1.02356
13.8819
];
figure(4);
subplot(3,1,2);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

X = [
0 0 
0.25 0 
0.5 0 
0.75 0 
1 0 
0 0.25 
0.25 0.25 
0.5 0.25 
0.75 0.25 
1 0.25 
0 0.5 
0.25 0.5 
0.5 0.5 
0.75 0.5 
1 0.5 
0 0.75 
0.25 0.75 
0.5 0.75 
0.75 0.75 
1 0.75 
0 1 
0.25 1 
0.5 1 
0.75 1 
1 1 
];
V = [
0.000552707 
0.244403 
0.475954 
0.679033 
0.841471 
0.244717 
0.555321 
0.850207 
1.11555 
1.33887 
0.477211 
0.851032 
1.20857 
1.53603 
1.8209 
0.6821 
1.11759 
1.5371 
1.92653 
2.27311 
0.848396 
1.34208 
1.82314 
2.27468 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-1.49812
-2.75116
-3.71609
-4.78162
-5.87042
-6.96472
-8.06033
-9.15626
-10.2523
-11.3483
-12.4443
-13.5404
-14.6364
-15.7324
-16.8284
-17.9245
-19.0205
-20.1165
-21.2126
-22.3086
-23.4046
-24.5007
-25.5967
];
figure(2);
subplot(4,1,1);
plot(R,'.');
title('Residual: n = 4');

X = [
0 0 
0.125 0 
0.25 0 
0.375 0 
0.5 0 
0.625 0 
0.75 0 
0.875 0 
1 0 
0 0.125 
0.125 0.125 
0.25 0.125 
0.375 0.125 
0.5 0.125 
0.625 0.125 
0.75 0.125 
0.875 0.125 
1 0.125 
0 0.25 
0.125 0.25 
0.25 0.25 
0.375 0.25 
0.5 0.25 
0.625 0.25 
0.75 0.25 
0.875 0.25 
1 0.25 
0 0.375 
0.125 0.375 
0.25 0.375 
0.375 0.375 
0.5 0.375 
0.625 0.375 
0.75 0.375 
0.875 0.375 
1 0.375 
0 0.5 
0.125 0.5 
0.25 0.5 
0.375 0.5 
0.5 0.5 
0.625 0.5 
0.75 0.5 
0.875 0.5 
1 0.5 
0 0.625 
0.125 0.625 
0.25 0.625 
0.375 0.625 
0.5 0.625 
0.625 0.625 
0.75 0.625 
0.875 0.625 
1 0.625 
0 0.75 
0.125 0.75 
0.25 0.75 
0.375 0.75 
0.5 0.75 
0.625 0.75 
0.75 0.75 
0.875 0.75 
1 0.75 
0 0.875 
0.125 0.875 
0.25 0.875 
0.375 0.875 
0.5 0.875 
0.625 0.875 
0.75 0.875 
0.875 0.875 
1 0.875 
0 1 
0.125 1 
0.25 1 
0.375 1 
0.5 1 
0.625 1 
0.75 1 
0.875 1 
1 1 
];
V = [
-0.00136843 
0.122866 
0.245569 
0.364554 
0.47789 
0.583797 
0.680634 
0.766932 
0.841471 
0.122869 
0.263283 
0.401746 
0.536391 
0.66536 
0.786886 
0.899327 
1.00119 
1.09115 
0.24558 
0.401754 
0.555927 
0.706233 
0.850833 
0.98797 
1.116 
1.23342 
1.33887 
0.364577 
0.536411 
0.706245 
0.872191 
1.03241 
1.18515 
1.32877 
1.46175 
1.58274 
0.477933 
0.665398 
0.850862 
1.03243 
1.20826 
1.3766 
1.5358 
1.68434 
1.8209 
0.583869 
0.786948 
0.988018 
1.18519 
1.37662 
1.56055 
1.73533 
1.89945 
2.05157 
0.680752 
0.899418 
1.11607 
1.32882 
1.53584 
1.73537 
1.92573 
2.10543 
2.27311 
0.767155 
1.00131 
1.23349 
1.46182 
1.68443 
1.89955 
2.10551 
2.30078 
2.48401 
0.842008 
1.09123 
1.3389 
1.58281 
1.82103 
2.05175 
2.27332 
2.48419 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.881693
-2.57933
-3.70001
-4.46421
-5.28228
-6.12747
-6.9859
-7.85086
-8.71906
-9.58886
-10.4595
-11.3305
-12.2017
-13.073
-13.9443
-14.8157
-15.6871
-16.5585
-17.4299
-18.3013
-19.1727
-20.0441
-20.9155
-21.7869
-22.6583
-23.5297
-24.4011
-25.2725
];
figure(2);
subplot(4,1,2);
plot(R,'.');
title('Residual: n = 8');

X = [
0 0 
0.0625 0 
0.125 0 
0.1875 0 
0.25 0 
0.3125 0 
0.375 0 
0.4375 0 
0.5 0 
0.5625 0 
0.625 0 
0.6875 0 
0.75 0 
0.8125 0 
0.875 0 
0.9375 0 
1 0 
0 0.0625 
0.0625 0.0625 
0.125 0.0625 
0.1875 0.0625 
0.25 0.0625 
0.3125 0.0625 
0.375 0.0625 
0.4375 0.0625 
0.5 0.0625 
0.5625 0.0625 
0.625 0.0625 
0.6875 0.0625 
0.75 0.0625 
0.8125 0.0625 
0.875 0.0625 
0.9375 0.0625 
1 0.0625 
0 0.125 
0.0625 0.125 
0.125 0.125 
0.1875 0.125 
0.25 0.125 
0.3125 0.125 
0.375 0.125 
0.4375 0.125 
0.5 0.125 
0.5625 0.125 
0.625 0.125 
0.6875 0.125 
0.75 0.125 
0.8125 0.125 
0.875 0.125 
0.9375 0.125 
1 0.125 
0 0.1875 
0.0625 0.1875 
0.125 0.1875 
0.1875 0.1875 
0.25 0.1875 
0.3125 0.1875 
0.375 0.1875 
0.4375 0.1875 
0.5 0.1875 
0.5625 0.1875 
0.625 0.1875 
0.6875 0.1875 
0.75 0.1875 
0.8125 0.1875 
0.875 0.1875 
0.9375 0.1875 
1 0.1875 
0 0.25 
0.0625 0.25 
0.125 0.25 
0.1875 0.25 
0.25 0.25 
0.3125 0.25 
0.375 0.25 
0.4375 0.25 
0.5 0.25 
0.5625 0.25 
0.625 0.25 
0.6875 0.25 
0.75 0.25 
0.8125 0.25 
0.875 0.25 
0.9375 0.25 
1 0.25 
0 0.3125 
0.0625 0.3125 
0.125 0.3125 
0.1875 0.3125 
0.25 0.3125 
0.3125 0.3125 
0.375 0.3125 
0.4375 0.3125 
0.5 0.3125 
0.5625 0.3125 
0.625 0.3125 
0.6875 0.3125 
0.75 0.3125 
0.8125 0.3125 
0.875 0.3125 
0.9375 0.3125 
1 0.3125 
0 0.375 
0.0625 0.375 
0.125 0.375 
0.1875 0.375 
0.25 0.375 
0.3125 0.375 
0.375 0.375 
0.4375 0.375 
0.5 0.375 
0.5625 0.375 
0.625 0.375 
0.6875 0.375 
0.75 0.375 
0.8125 0.375 
0.875 0.375 
0.9375 0.375 
1 0.375 
0 0.4375 
0.0625 0.4375 
0.125 0.4375 
0.1875 0.4375 
0.25 0.4375 
0.3125 0.4375 
0.375 0.4375 
0.4375 0.4375 
0.5 0.4375 
0.5625 0.4375 
0.625 0.4375 
0.6875 0.4375 
0.75 0.4375 
0.8125 0.4375 
0.875 0.4375 
0.9375 0.4375 
1 0.4375 
0 0.5 
0.0625 0.5 
0.125 0.5 
0.1875 0.5 
0.25 0.5 
0.3125 0.5 
0.375 0.5 
0.4375 0.5 
0.5 0.5 
0.5625 0.5 
0.625 0.5 
0.6875 0.5 
0.75 0.5 
0.8125 0.5 
0.875 0.5 
0.9375 0.5 
1 0.5 
0 0.5625 
0.0625 0.5625 
0.125 0.5625 
0.1875 0.5625 
0.25 0.5625 
0.3125 0.5625 
0.375 0.5625 
0.4375 0.5625 
0.5 0.5625 
0.5625 0.5625 
0.625 0.5625 
0.6875 0.5625 
0.75 0.5625 
0.8125 0.5625 
0.875 0.5625 
0.9375 0.5625 
1 0.5625 
0 0.625 
0.0625 0.625 
0.125 0.625 
0.1875 0.625 
0.25 0.625 
0.3125 0.625 
0.375 0.625 
0.4375 0.625 
0.5 0.625 
0.5625 0.625 
0.625 0.625 
0.6875 0.625 
0.75 0.625 
0.8125 0.625 
0.875 0.625 
0.9375 0.625 
1 0.625 
0 0.6875 
0.0625 0.6875 
0.125 0.6875 
0.1875 0.6875 
0.25 0.6875 
0.3125 0.6875 
0.375 0.6875 
0.4375 0.6875 
0.5 0.6875 
0.5625 0.6875 
0.625 0.6875 
0.6875 0.6875 
0.75 0.6875 
0.8125 0.6875 
0.875 0.6875 
0.9375 0.6875 
1 0.6875 
0 0.75 
0.0625 0.75 
0.125 0.75 
0.1875 0.75 
0.25 0.75 
0.3125 0.75 
0.375 0.75 
0.4375 0.75 
0.5 0.75 
0.5625 0.75 
0.625 0.75 
0.6875 0.75 
0.75 0.75 
0.8125 0.75 
0.875 0.75 
0.9375 0.75 
1 0.75 
0 0.8125 
0.0625 0.8125 
0.125 0.8125 
0.1875 0.8125 
0.25 0.8125 
0.3125 0.8125 
0.375 0.8125 
0.4375 0.8125 
0.5 0.8125 
0.5625 0.8125 
0.625 0.8125 
0.6875 0.8125 
0.75 0.8125 
0.8125 0.8125 
0.875 0.8125 
0.9375 0.8125 
1 0.8125 
0 0.875 
0.0625 0.875 
0.125 0.875 
0.1875 0.875 
0.25 0.875 
0.3125 0.875 
0.375 0.875 
0.4375 0.875 
0.5 0.875 
0.5625 0.875 
0.625 0.875 
0.6875 0.875 
0.75 0.875 
0.8125 0.875 
0.875 0.875 
0.9375 0.875 
1 0.875 
0 0.9375 
0.0625 0.9375 
0.125 0.9375 
0.1875 0.9375 
0.25 0.9375 
0.3125 0.9375 
0.375 0.9375 
0.4375 0.9375 
0.5 0.9375 
0.5625 0.9375 
0.625 0.9375 
0.6875 0.9375 
0.75 0.9375 
0.8125 0.9375 
0.875 0.9375 
0.9375 0.9375 
1 0.9375 
0 1 
0.0625 1 
0.125 1 
0.1875 1 
0.25 1 
0.3125 1 
0.375 1 
0.4375 1 
0.5 1 
0.5625 1 
0.625 1 
0.6875 1 
0.75 1 
0.8125 1 
0.875 1 
0.9375 1 
1 1 
];
V = [
-0.000576163 
0.0618282 
0.124041 
0.185786 
0.24681 
0.306873 
0.365738 
0.423176 
0.478961 
0.532877 
0.584712 
0.634266 
0.681346 
0.72577 
0.767366 
0.805978 
0.841471 
0.0618279 
0.128208 
0.194345 
0.26 
0.324933 
0.388902 
0.451674 
0.513018 
0.57271 
0.630531 
0.686273 
0.739733 
0.790718 
0.839046 
0.884546 
0.927057 
0.96643 
0.12404 
0.194344 
0.264398 
0.333966 
0.402807 
0.470685 
0.537364 
0.602614 
0.666212 
0.727939 
0.787586 
0.844951 
0.89984 
0.952072 
1.00147 
1.04788 
1.09115 
0.185783 
0.259998 
0.333964 
0.407442 
0.480193 
0.551978 
0.622564 
0.69172 
0.759224 
0.824857 
0.888409 
0.949678 
1.00847 
1.06461 
1.11791 
1.16821 
1.21537 
0.246805 
0.324928 
0.402803 
0.480191 
0.556849 
0.632542 
0.707034 
0.780097 
0.851506 
0.921044 
0.9885 
1.05367 
1.11637 
1.17641 
1.23361 
1.28782 
1.33887 
0.306865 
0.388895 
0.470678 
0.551973 
0.632539 
0.712138 
0.790537 
0.867505 
0.94282 
1.01626 
1.08762 
1.1567 
1.2233 
1.28724 
1.34834 
1.40645 
1.46141 
0.365726 
0.451663 
0.537353 
0.622555 
0.707028 
0.790533 
0.872838 
0.953712 
1.03293 
1.11028 
1.18554 
1.25852 
1.32903 
1.39687 
1.46188 
1.52388 
1.58274 
0.42316 
0.513002 
0.602599 
0.691707 
0.780086 
0.867498 
0.953708 
1.03849 
1.12161 
1.20286 
1.28203 
1.35892 
1.43332 
1.50507 
1.57398 
1.63989 
1.70265 
0.47894 
0.572689 
0.666192 
0.759206 
0.851491 
0.942808 
1.03292 
1.12161 
1.20864 
1.29379 
1.37687 
1.45765 
1.53596 
1.61161 
1.68442 
1.75423 
1.8209 
0.53285 
0.630505 
0.727913 
0.824833 
0.921023 
1.01625 
1.11027 
1.20286 
1.29379 
1.38285 
1.46983 
1.55452 
1.63673 
1.71628 
1.79299 
1.86671 
1.93727 
0.584679 
0.68624 
0.787554 
0.888379 
0.988474 
1.0876 
1.18553 
1.28202 
1.37686 
1.46982 
1.5607 
1.6493 
1.73542 
1.81887 
1.89948 
1.9771 
2.05157 
0.634225 
0.739692 
0.844911 
0.949641 
1.05364 
1.15667 
1.2585 
1.3589 
1.45764 
1.55451 
1.6493 
1.7418 
1.83182 
1.91917 
2.00369 
2.08521 
2.16358 
0.681296 
0.790668 
0.899792 
1.00843 
1.11633 
1.22327 
1.329 
1.4333 
1.53595 
1.63672 
1.73541 
1.83181 
1.92574 
2.017 
2.10542 
2.19084 
2.27311 
0.72571 
0.838987 
0.952013 
1.06455 
1.17636 
1.2872 
1.39683 
1.50504 
1.61159 
1.71627 
1.81886 
1.91917 
2.017 
2.11216 
2.20448 
2.29381 
2.37998 
0.767298 
0.884475 
1.0014 
1.11784 
1.23355 
1.34829 
1.46183 
1.57395 
1.6844 
1.79298 
1.89948 
2.00369 
2.10542 
2.20449 
2.30072 
2.39394 
2.48401 
0.805906 
0.926973 
1.04779 
1.16813 
1.28774 
1.40639 
1.52384 
1.63985 
1.75421 
1.8667 
1.9771 
2.08522 
2.19085 
2.29382 
2.39395 
2.49108 
2.58505 
0.84142 
0.966324 
1.09103 
1.21527 
1.33879 
1.46134 
1.58269 
1.70261 
1.82088 
1.93727 
2.05158 
2.1636 
2.27314 
2.38001 
2.48405 
2.58508 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.540641
-2.05973
-3.45693
-4.72187
-5.74993
-6.57592
-7.25503
-7.92021
-8.60441
-9.3006
-10.0044
-10.7132
-11.4252
-12.1392
-12.8545
-13.5708
-14.2876
-15.0047
-15.7221
-16.4397
-17.1574
-17.8751
-18.5929
-19.3107
-20.0286
-20.7464
-21.4643
-22.1822
-22.9
-23.6179
-24.3358
-25.0536
-25.7715
];
figure(2);
subplot(4,1,3);
plot(R,'.');
title('Residual: n = 16');

X = [
0 0 
0.03125 0 
0.0625 0 
0.09375 0 
0.125 0 
0.15625 0 
0.1875 0 
0.21875 0 
0.25 0 
0.28125 0 
0.3125 0 
0.34375 0 
0.375 0 
0.40625 0 
0.4375 0 
0.46875 0 
0.5 0 
0.53125 0 
0.5625 0 
0.59375 0 
0.625 0 
0.65625 0 
0.6875 0 
0.71875 0 
0.75 0 
0.78125 0 
0.8125 0 
0.84375 0 
0.875 0 
0.90625 0 
0.9375 0 
0.96875 0 
1 0 
0 0.03125 
0.03125 0.03125 
0.0625 0.03125 
0.09375 0.03125 
0.125 0.03125 
0.15625 0.03125 
0.1875 0.03125 
0.21875 0.03125 
0.25 0.03125 
0.28125 0.03125 
0.3125 0.03125 
0.34375 0.03125 
0.375 0.03125 
0.40625 0.03125 
0.4375 0.03125 
0.46875 0.03125 
0.5 0.03125 
0.53125 0.03125 
0.5625 0.03125 
0.59375 0.03125 
0.625 0.03125 
0.65625 0.03125 
0.6875 0.03125 
0.71875 0.03125 
0.75 0.03125 
0.78125 0.03125 
0.8125 0.03125 
0.84375 0.03125 
0.875 0.03125 
0.90625 0.03125 
0.9375 0.03125 
0.96875 0.03125 
1 0.03125 
0 0.0625 
0.03125 0.0625 
0.0625 0.0625 
0.09375 0.0625 
0.125 0.0625 
0.15625 0.0625 
0.1875 0.0625 
0.21875 0.0625 
0.25 0.0625 
0.28125 0.0625 
0.3125 0.0625 
0.34375 0.0625 
0.375 0.0625 
0.40625 0.0625 
0.4375 0.0625 
0.46875 0.0625 
0.5 0.0625 
0.53125 0.0625 
0.5625 0.0625 
0.59375 0.0625 
0.625 0.0625 
0.65625 0.0625 
0.6875 0.0625 
0.71875 0.0625 
0.75 0.0625 
0.78125 0.0625 
0.8125 0.0625 
0.84375 0.0625 
0.875 0.0625 
0.90625 0.0625 
0.9375 0.0625 
0.96875 0.0625 
1 0.0625 
0 0.09375 
0.03125 0.09375 
0.0625 0.09375 
0.09375 0.09375 
0.125 0.09375 
0.15625 0.09375 
0.1875 0.09375 
0.21875 0.09375 
0.25 0.09375 
0.28125 0.09375 
0.3125 0.09375 
0.34375 0.09375 
0.375 0.09375 
0.40625 0.09375 
0.4375 0.09375 
0.46875 0.09375 
0.5 0.09375 
0.53125 0.09375 
0.5625 0.09375 
0.59375 0.09375 
0.625 0.09375 
0.65625 0.09375 
0.6875 0.09375 
0.71875 0.09375 
0.75 0.09375 
0.78125 0.09375 
0.8125 0.09375 
0.84375 0.09375 
0.875 0.09375 
0.90625 0.09375 
0.9375 0.09375 
0.96875 0.09375 
1 0.09375 
0 0.125 
0.03125 0.125 
0.0625 0.125 
0.09375 0.125 
0.125 0.125 
0.15625 0.125 
0.1875 0.125 
0.21875 0.125 
0.25 0.125 
0.28125 0.125 
0.3125 0.125 
0.34375 0.125 
0.375 0.125 
0.40625 0.125 
0.4375 0.125 
0.46875 0.125 
0.5 0.125 
0.53125 0.125 
0.5625 0.125 
0.59375 0.125 
0.625 0.125 
0.65625 0.125 
0.6875 0.125 
0.71875 0.125 
0.75 0.125 
0.78125 0.125 
0.8125 0.125 
0.84375 0.125 
0.875 0.125 
0.90625 0.125 
0.9375 0.125 
0.96875 0.125 
1 0.125 
0 0.15625 
0.03125 0.15625 
0.0625 0.15625 
0.09375 0.15625 
0.125 0.15625 
0.15625 0.15625 
0.1875 0.15625 
0.21875 0.15625 
0.25 0.15625 
0.28125 0.15625 
0.3125 0.15625 
0.34375 0.15625 
0.375 0.15625 
0.40625 0.15625 
0.4375 0.15625 
0.46875 0.15625 
0.5 0.15625 
0.53125 0.15625 
0.5625 0.15625 
0.59375 0.15625 
0.625 0.15625 
0.65625 0.15625 
0.6875 0.15625 
0.71875 0.15625 
0.75 0.15625 
0.78125 0.15625 
0.8125 0.15625 
0.84375 0.15625 
0.875 0.15625 
0.90625 0.15625 
0.9375 0.15625 
0.96875 0.15625 
1 0.15625 
0 0.1875 
0.03125 0.1875 
0.0625 0.1875 
0.09375 0.1875 
0.125 0.1875 
0.15625 0.1875 
0.1875 0.1875 
0.21875 0.1875 
0.25 0.1875 
0.28125 0.1875 
0.3125 0.1875 
0.34375 0.1875 
0.375 0.1875 
0.40625 0.1875 
0.4375 0.1875 
0.46875 0.1875 
0.5 0.1875 
0.53125 0.1875 
0.5625 0.1875 
0.59375 0.1875 
0.625 0.1875 
0.65625 0.1875 
0.6875 0.1875 
0.71875 0.1875 
0.75 0.1875 
0.78125 0.1875 
0.8125 0.1875 
0.84375 0.1875 
0.875 0.1875 
0.90625 0.1875 
0.9375 0.1875 
0.96875 0.1875 
1 0.1875 
0 0.21875 
0.03125 0.21875 
0.0625 0.21875 
0.09375 0.21875 
0.125 0.21875 
0.15625 0.21875 
0.1875 0.21875 
0.21875 0.21875 
0.25 0.21875 
0.28125 0.21875 
0.3125 0.21875 
0.34375 0.21875 
0.375 0.21875 
0.40625 0.21875 
0.4375 0.21875 
0.46875 0.21875 
0.5 0.21875 
0.53125 0.21875 
0.5625 0.21875 
0.59375 0.21875 
0.625 0.21875 
0.65625 0.21875 
0.6875 0.21875 
0.71875 0.21875 
0.75 0.21875 
0.78125 0.21875 
0.8125 0.21875 
0.84375 0.21875 
0.875 0.21875 
0.90625 0.21875 
0.9375 0.21875 
0.96875 0.21875 
1 0.21875 
0 0.25 
0.03125 0.25 
0.0625 0.25 
0.09375 0.25 
0.125 0.25 
0.15625 0.25 
0.1875 0.25 
0.21875 0.25 
0.25 0.25 
0.28125 0.25 
0.3125 0.25 
0.34375 0.25 
0.375 0.25 
0.40625 0.25 
0.4375 0.25 
0.46875 0.25 
0.5 0.25 
0.53125 0.25 
0.5625 0.25 
0.59375 0.25 
0.625 0.25 
0.65625 0.25 
0.6875 0.25 
0.71875 0.25 
0.75 0.25 
0.78125 0.25 
0.8125 0.25 
0.84375 0.25 
0.875 0.25 
0.90625 0.25 
0.9375 0.25 
0.96875 0.25 
1 0.25 
0 0.28125 
0.03125 0.28125 
0.0625 0.28125 
0.09375 0.28125 
0.125 0.28125 
0.15625 0.28125 
0.1875 0.28125 
0.21875 0.28125 
0.25 0.28125 
0.28125 0.28125 
0.3125 0.28125 
0.34375 0.28125 
0.375 0.28125 
0.40625 0.28125 
0.4375 0.28125 
0.46875 0.28125 
0.5 0.28125 
0.53125 0.28125 
0.5625 0.28125 
0.59375 0.28125 
0.625 0.28125 
0.65625 0.28125 
0.6875 0.28125 
0.71875 0.28125 
0.75 0.28125 
0.78125 0.28125 
0.8125 0.28125 
0.84375 0.28125 
0.875 0.28125 
0.90625 0.28125 
0.9375 0.28125 
0.96875 0.28125 
1 0.28125 
0 0.3125 
0.03125 0.3125 
0.0625 0.3125 
0.09375 0.3125 
0.125 0.3125 
0.15625 0.3125 
0.1875 0.3125 
0.21875 0.3125 
0.25 0.3125 
0.28125 0.3125 
0.3125 0.3125 
0.34375 0.3125 
0.375 0.3125 
0.40625 0.3125 
0.4375 0.3125 
0.46875 0.3125 
0.5 0.3125 
0.53125 0.3125 
0.5625 0.3125 
0.59375 0.3125 
0.625 0.3125 
0.65625 0.3125 
0.6875 0.3125 
0.71875 0.3125 
0.75 0.3125 
0.78125 0.3125 
0.8125 0.3125 
0.84375 0.3125 
0.875 0.3125 
0.90625 0.3125 
0.9375 0.3125 
0.96875 0.3125 
1 0.3125 
0 0.34375 
0.03125 0.34375 
0.0625 0.34375 
0.09375 0.34375 
0.125 0.34375 
0.15625 0.34375 
0.1875 0.34375 
0.21875 0.34375 
0.25 0.34375 
0.28125 0.34375 
0.3125 0.34375 
0.34375 0.34375 
0.375 0.34375 
0.40625 0.34375 
0.4375 0.34375 
0.46875 0.34375 
0.5 0.34375 
0.53125 0.34375 
0.5625 0.34375 
0.59375 0.34375 
0.625 0.34375 
0.65625 0.34375 
0.6875 0.34375 
0.71875 0.34375 
0.75 0.34375 
0.78125 0.34375 
0.8125 0.34375 
0.84375 0.34375 
0.875 0.34375 
0.90625 0.34375 
0.9375 0.34375 
0.96875 0.34375 
1 0.34375 
0 0.375 
0.03125 0.375 
0.0625 0.375 
0.09375 0.375 
0.125 0.375 
0.15625 0.375 
0.1875 0.375 
0.21875 0.375 
0.25 0.375 
0.28125 0.375 
0.3125 0.375 
0.34375 0.375 
0.375 0.375 
0.40625 0.375 
0.4375 0.375 
0.46875 0.375 
0.5 0.375 
0.53125 0.375 
0.5625 0.375 
0.59375 0.375 
0.625 0.375 
0.65625 0.375 
0.6875 0.375 
0.71875 0.375 
0.75 0.375 
0.78125 0.375 
0.8125 0.375 
0.84375 0.375 
0.875 0.375 
0.90625 0.375 
0.9375 0.375 
0.96875 0.375 
1 0.375 
0 0.40625 
0.03125 0.40625 
0.0625 0.40625 
0.09375 0.40625 
0.125 0.40625 
0.15625 0.40625 
0.1875 0.40625 
0.21875 0.40625 
0.25 0.40625 
0.28125 0.40625 
0.3125 0.40625 
0.34375 0.40625 
0.375 0.40625 
0.40625 0.40625 
0.4375 0.40625 
0.46875 0.40625 
0.5 0.40625 
0.53125 0.40625 
0.5625 0.40625 
0.59375 0.40625 
0.625 0.40625 
0.65625 0.40625 
0.6875 0.40625 
0.71875 0.40625 
0.75 0.40625 
0.78125 0.40625 
0.8125 0.40625 
0.84375 0.40625 
0.875 0.40625 
0.90625 0.40625 
0.9375 0.40625 
0.96875 0.40625 
1 0.40625 
0 0.4375 
0.03125 0.4375 
0.0625 0.4375 
0.09375 0.4375 
0.125 0.4375 
0.15625 0.4375 
0.1875 0.4375 
0.21875 0.4375 
0.25 0.4375 
0.28125 0.4375 
0.3125 0.4375 
0.34375 0.4375 
0.375 0.4375 
0.40625 0.4375 
0.4375 0.4375 
0.46875 0.4375 
0.5 0.4375 
0.53125 0.4375 
0.5625 0.4375 
0.59375 0.4375 
0.625 0.4375 
0.65625 0.4375 
0.6875 0.4375 
0.71875 0.4375 
0.75 0.4375 
0.78125 0.4375 
0.8125 0.4375 
0.84375 0.4375 
0.875 0.4375 
0.90625 0.4375 
0.9375 0.4375 
0.96875 0.4375 
1 0.4375 
0 0.46875 
0.03125 0.46875 
0.0625 0.46875 
0.09375 0.46875 
0.125 0.46875 
0.15625 0.46875 
0.1875 0.46875 
0.21875 0.46875 
0.25 0.46875 
0.28125 0.46875 
0.3125 0.46875 
0.34375 0.46875 
0.375 0.46875 
0.40625 0.46875 
0.4375 0.46875 
0.46875 0.46875 
0.5 0.46875 
0.53125 0.46875 
0.5625 0.46875 
0.59375 0.46875 
0.625 0.46875 
0.65625 0.46875 
0.6875 0.46875 
0.71875 0.46875 
0.75 0.46875 
0.78125 0.46875 
0.8125 0.46875 
0.84375 0.46875 
0.875 0.46875 
0.90625 0.46875 
0.9375 0.46875 
0.96875 0.46875 
1 0.46875 
0 0.5 
0.03125 0.5 
0.0625 0.5 
0.09375 0.5 
0.125 0.5 
0.15625 0.5 
0.1875 0.5 
0.21875 0.5 
0.25 0.5 
0.28125 0.5 
0.3125 0.5 
0.34375 0.5 
0.375 0.5 
0.40625 0.5 
0.4375 0.5 
0.46875 0.5 
0.5 0.5 
0.53125 0.5 
0.5625 0.5 
0.59375 0.5 
0.625 0.5 
0.65625 0.5 
0.6875 0.5 
0.71875 0.5 
0.75 0.5 
0.78125 0.5 
0.8125 0.5 
0.84375 0.5 
0.875 0.5 
0.90625 0.5 
0.9375 0.5 
0.96875 0.5 
1 0.5 
0 0.53125 
0.03125 0.53125 
0.0625 0.53125 
0.09375 0.53125 
0.125 0.53125 
0.15625 0.53125 
0.1875 0.53125 
0.21875 0.53125 
0.25 0.53125 
0.28125 0.53125 
0.3125 0.53125 
0.34375 0.53125 
0.375 0.53125 
0.40625 0.53125 
0.4375 0.53125 
0.46875 0.53125 
0.5 0.53125 
0.53125 0.53125 
0.5625 0.53125 
0.59375 0.53125 
0.625 0.53125 
0.65625 0.53125 
0.6875 0.53125 
0.71875 0.53125 
0.75 0.53125 
0.78125 0.53125 
0.8125 0.53125 
0.84375 0.53125 
0.875 0.53125 
0.90625 0.53125 
0.9375 0.53125 
0.96875 0.53125 
1 0.53125 
0 0.5625 
0.03125 0.5625 
0.0625 0.5625 
0.09375 0.5625 
0.125 0.5625 
0.15625 0.5625 
0.1875 0.5625 
0.21875 0.5625 
0.25 0.5625 
0.28125 0.5625 
0.3125 0.5625 
0.34375 0.5625 
0.375 0.5625 
0.40625 0.5625 
0.4375 0.5625 
0.46875 0.5625 
0.5 0.5625 
0.53125 0.5625 
0.5625 0.5625 
0.59375 0.5625 
0.625 0.5625 
0.65625 0.5625 
0.6875 0.5625 
0.71875 0.5625 
0.75 0.5625 
0.78125 0.5625 
0.8125 0.5625 
0.84375 0.5625 
0.875 0.5625 
0.90625 0.5625 
0.9375 0.5625 
0.96875 0.5625 
1 0.5625 
0 0.59375 
0.03125 0.59375 
0.0625 0.59375 
0.09375 0.59375 
0.125 0.59375 
0.15625 0.59375 
0.1875 0.59375 
0.21875 0.59375 
0.25 0.59375 
0.28125 0.59375 
0.3125 0.59375 
0.34375 0.59375 
0.375 0.59375 
0.40625 0.59375 
0.4375 0.59375 
0.46875 0.59375 
0.5 0.59375 
0.53125 0.59375 
0.5625 0.59375 
0.59375 0.59375 
0.625 0.59375 
0.65625 0.59375 
0.6875 0.59375 
0.71875 0.59375 
0.75 0.59375 
0.78125 0.59375 
0.8125 0.59375 
0.84375 0.59375 
0.875 0.59375 
0.90625 0.59375 
0.9375 0.59375 
0.96875 0.59375 
1 0.59375 
0 0.625 
0.03125 0.625 
0.0625 0.625 
0.09375 0.625 
0.125 0.625 
0.15625 0.625 
0.1875 0.625 
0.21875 0.625 
0.25 0.625 
0.28125 0.625 
0.3125 0.625 
0.34375 0.625 
0.375 0.625 
0.40625 0.625 
0.4375 0.625 
0.46875 0.625 
0.5 0.625 
0.53125 0.625 
0.5625 0.625 
0.59375 0.625 
0.625 0.625 
0.65625 0.625 
0.6875 0.625 
0.71875 0.625 
0.75 0.625 
0.78125 0.625 
0.8125 0.625 
0.84375 0.625 
0.875 0.625 
0.90625 0.625 
0.9375 0.625 
0.96875 0.625 
1 0.625 
0 0.65625 
0.03125 0.65625 
0.0625 0.65625 
0.09375 0.65625 
0.125 0.65625 
0.15625 0.65625 
0.1875 0.65625 
0.21875 0.65625 
0.25 0.65625 
0.28125 0.65625 
0.3125 0.65625 
0.34375 0.65625 
0.375 0.65625 
0.40625 0.65625 
0.4375 0.65625 
0.46875 0.65625 
0.5 0.65625 
0.53125 0.65625 
0.5625 0.65625 
0.59375 0.65625 
0.625 0.65625 
0.65625 0.65625 
0.6875 0.65625 
0.71875 0.65625 
0.75 0.65625 
0.78125 0.65625 
0.8125 0.65625 
0.84375 0.65625 
0.875 0.65625 
0.90625 0.65625 
0.9375 0.65625 
0.96875 0.65625 
1 0.65625 
0 0.6875 
0.03125 0.6875 
0.0625 0.6875 
0.09375 0.6875 
0.125 0.6875 
0.15625 0.6875 
0.1875 0.6875 
0.21875 0.6875 
0.25 0.6875 
0.28125 0.6875 
0.3125 0.6875 
0.34375 0.6875 
0.375 0.6875 
0.40625 0.6875 
0.4375 0.6875 
0.46875 0.6875 
0.5 0.6875 
0.53125 0.6875 
0.5625 0.6875 
0.59375 0.6875 
0.625 0.6875 
0.65625 0.6875 
0.6875 0.6875 
0.71875 0.6875 
0.75 0.6875 
0.78125 0.6875 
0.8125 0.6875 
0.84375 0.6875 
0.875 0.6875 
0.90625 0.6875 
0.9375 0.6875 
0.96875 0.6875 
1 0.6875 
0 0.71875 
0.03125 0.71875 
0.0625 0.71875 
0.09375 0.71875 
0.125 0.71875 
0.15625 0.71875 
0.1875 0.71875 
0.21875 0.71875 
0.25 0.71875 
0.28125 0.71875 
0.3125 0.71875 
0.34375 0.71875 
0.375 0.71875 
0.40625 0.71875 
0.4375 0.71875 
0.46875 0.71875 
0.5 0.71875 
0.53125 0.71875 
0.5625 0.71875 
0.59375 0.71875 
0.625 0.71875 
0.65625 0.71875 
0.6875 0.71875 
0.71875 0.71875 
0.75 0.71875 
0.78125 0.71875 
0.8125 0.71875 
0.84375 0.71875 
0.875 0.71875 
0.90625 0.71875 
0.9375 0.71875 
0.96875 0.71875 
1 0.71875 
0 0.75 
0.03125 0.75 
0.0625 0.75 
0.09375 0.75 
0.125 0.75 
0.15625 0.75 
0.1875 0.75 
0.21875 0.75 
0.25 0.75 
0.28125 0.75 
0.3125 0.75 
0.34375 0.75 
0.375 0.75 
0.40625 0.75 
0.4375 0.75 
0.46875 0.75 
0.5 0.75 
0.53125 0.75 
0.5625 0.75 
0.59375 0.75 
0.625 0.75 
0.65625 0.75 
0.6875 0.75 
0.71875 0.75 
0.75 0.75 
0.78125 0.75 
0.8125 0.75 
0.84375 0.75 
0.875 0.75 
0.90625 0.75 
0.9375 0.75 
0.96875 0.75 
1 0.75 
0 0.78125 
0.03125 0.78125 
0.0625 0.78125 
0.09375 0.78125 
0.125 0.78125 
0.15625 0.78125 
0.1875 0.78125 
0.21875 0.78125 
0.25 0.78125 
0.28125 0.78125 
0.3125 0.78125 
0.34375 0.78125 
0.375 0.78125 
0.40625 0.78125 
0.4375 0.78125 
0.46875 0.78125 
0.5 0.78125 
0.53125 0.78125 
0.5625 0.78125 
0.59375 0.78125 
0.625 0.78125 
0.65625 0.78125 
0.6875 0.78125 
0.71875 0.78125 
0.75 0.78125 
0.78125 0.78125 
0.8125 0.78125 
0.84375 0.78125 
0.875 0.78125 
0.90625 0.78125 
0.9375 0.78125 
0.96875 0.78125 
1 0.78125 
0 0.8125 
0.03125 0.8125 
0.0625 0.8125 
0.09375 0.8125 
0.125 0.8125 
0.15625 0.8125 
0.1875 0.8125 
0.21875 0.8125 
0.25 0.8125 
0.28125 0.8125 
0.3125 0.8125 
0.34375 0.8125 
0.375 0.8125 
0.40625 0.8125 
0.4375 0.8125 
0.46875 0.8125 
0.5 0.8125 
0.53125 0.8125 
0.5625 0.8125 
0.59375 0.8125 
0.625 0.8125 
0.65625 0.8125 
0.6875 0.8125 
0.71875 0.8125 
0.75 0.8125 
0.78125 0.8125 
0.8125 0.8125 
0.84375 0.8125 
0.875 0.8125 
0.90625 0.8125 
0.9375 0.8125 
0.96875 0.8125 
1 0.8125 
0 0.84375 
0.03125 0.84375 
0.0625 0.84375 
0.09375 0.84375 
0.125 0.84375 
0.15625 0.84375 
0.1875 0.84375 
0.21875 0.84375 
0.25 0.84375 
0.28125 0.84375 
0.3125 0.84375 
0.34375 0.84375 
0.375 0.84375 
0.40625 0.84375 
0.4375 0.84375 
0.46875 0.84375 
0.5 0.84375 
0.53125 0.84375 
0.5625 0.84375 
0.59375 0.84375 
0.625 0.84375 
0.65625 0.84375 
0.6875 0.84375 
0.71875 0.84375 
0.75 0.84375 
0.78125 0.84375 
0.8125 0.84375 
0.84375 0.84375 
0.875 0.84375 
0.90625 0.84375 
0.9375 0.84375 
0.96875 0.84375 
1 0.84375 
0 0.875 
0.03125 0.875 
0.0625 0.875 
0.09375 0.875 
0.125 0.875 
0.15625 0.875 
0.1875 0.875 
0.21875 0.875 
0.25 0.875 
0.28125 0.875 
0.3125 0.875 
0.34375 0.875 
0.375 0.875 
0.40625 0.875 
0.4375 0.875 
0.46875 0.875 
0.5 0.875 
0.53125 0.875 
0.5625 0.875 
0.59375 0.875 
0.625 0.875 
0.65625 0.875 
0.6875 0.875 
0.71875 0.875 
0.75 0.875 
0.78125 0.875 
0.8125 0.875 
0.84375 0.875 
0.875 0.875 
0.90625 0.875 
0.9375 0.875 
0.96875 0.875 
1 0.875 
0 0.90625 
0.03125 0.90625 
0.0625 0.90625 
0.09375 0.90625 
0.125 0.90625 
0.15625 0.90625 
0.1875 0.90625 
0.21875 0.90625 
0.25 0.90625 
0.28125 0.90625 
0.3125 0.90625 
0.34375 0.90625 
0.375 0.90625 
0.40625 0.90625 
0.4375 0.90625 
0.46875 0.90625 
0.5 0.90625 
0.53125 0.90625 
0.5625 0.90625 
0.59375 0.90625 
0.625 0.90625 
0.65625 0.90625 
0.6875 0.90625 
0.71875 0.90625 
0.75 0.90625 
0.78125 0.90625 
0.8125 0.90625 
0.84375 0.90625 
0.875 0.90625 
0.90625 0.90625 
0.9375 0.90625 
0.96875 0.90625 
1 0.90625 
0 0.9375 
0.03125 0.9375 
0.0625 0.9375 
0.09375 0.9375 
0.125 0.9375 
0.15625 0.9375 
0.1875 0.9375 
0.21875 0.9375 
0.25 0.9375 
0.28125 0.9375 
0.3125 0.9375 
0.34375 0.9375 
0.375 0.9375 
0.40625 0.9375 
0.4375 0.9375 
0.46875 0.9375 
0.5 0.9375 
0.53125 0.9375 
0.5625 0.9375 
0.59375 0.9375 
0.625 0.9375 
0.65625 0.9375 
0.6875 0.9375 
0.71875 0.9375 
0.75 0.9375 
0.78125 0.9375 
0.8125 0.9375 
0.84375 0.9375 
0.875 0.9375 
0.90625 0.9375 
0.9375 0.9375 
0.96875 0.9375 
1 0.9375 
0 0.96875 
0.03125 0.96875 
0.0625 0.96875 
0.09375 0.96875 
0.125 0.96875 
0.15625 0.96875 
0.1875 0.96875 
0.21875 0.96875 
0.25 0.96875 
0.28125 0.96875 
0.3125 0.96875 
0.34375 0.96875 
0.375 0.96875 
0.40625 0.96875 
0.4375 0.96875 
0.46875 0.96875 
0.5 0.96875 
0.53125 0.96875 
0.5625 0.96875 
0.59375 0.96875 
0.625 0.96875 
0.65625 0.96875 
0.6875 0.96875 
0.71875 0.96875 
0.75 0.96875 
0.78125 0.96875 
0.8125 0.96875 
0.84375 0.96875 
0.875 0.96875 
0.90625 0.96875 
0.9375 0.96875 
0.96875 0.96875 
1 0.96875 
0 1 
0.03125 1 
0.0625 1 
0.09375 1 
0.125 1 
0.15625 1 
0.1875 1 
0.21875 1 
0.25 1 
0.28125 1 
0.3125 1 
0.34375 1 
0.375 1 
0.40625 1 
0.4375 1 
0.46875 1 
0.5 1 
0.53125 1 
0.5625 1 
0.59375 1 
0.625 1 
0.65625 1 
0.6875 1 
0.71875 1 
0.75 1 
0.78125 1 
0.8125 1 
0.84375 1 
0.875 1 
0.90625 1 
0.9375 1 
0.96875 1 
1 1 
];
V = [
-0.000178493 
0.0310595 
0.0622736 
0.093429 
0.124494 
0.155438 
0.18623 
0.21684 
0.247239 
0.277396 
0.307283 
0.336869 
0.366126 
0.395026 
0.42354 
0.45164 
0.4793 
0.506491 
0.533188 
0.559364 
0.584994 
0.610053 
0.634516 
0.65836 
0.681561 
0.704097 
0.725945 
0.747085 
0.767496 
0.787159 
0.806053 
0.824163 
0.841471 
0.0310595 
0.0632828 
0.0954756 
0.127608 
0.15965 
0.19157 
0.223339 
0.254926 
0.286301 
0.317435 
0.348298 
0.378861 
0.409095 
0.438971 
0.468462 
0.497539 
0.526175 
0.554342 
0.582016 
0.609168 
0.635775 
0.66181 
0.68725 
0.71207 
0.736248 
0.75976 
0.782585 
0.804702 
0.82609 
0.846728 
0.866599 
0.885684 
0.903966 
0.0622735 
0.0954755 
0.128646 
0.161756 
0.194775 
0.227672 
0.260418 
0.292981 
0.325333 
0.357444 
0.389283 
0.420822 
0.452033 
0.482886 
0.513353 
0.543406 
0.573019 
0.602163 
0.630813 
0.658942 
0.686525 
0.713537 
0.739954 
0.76575 
0.790904 
0.815393 
0.839195 
0.862288 
0.884652 
0.906267 
0.927114 
0.947174 
0.96643 
0.0934287 
0.127608 
0.161756 
0.195843 
0.229839 
0.263713 
0.297435 
0.330975 
0.364304 
0.397391 
0.430207 
0.462723 
0.49491 
0.526739 
0.558183 
0.589213 
0.619802 
0.649923 
0.679549 
0.708655 
0.737215 
0.765203 
0.792596 
0.819369 
0.8455 
0.870965 
0.895743 
0.919812 
0.943152 
0.965743 
0.987566 
1.0086 
1.02883 
0.124493 
0.159649 
0.194775 
0.229839 
0.264811 
0.299662 
0.334361 
0.368878 
0.403183 
0.437246 
0.471039 
0.504532 
0.537695 
0.570501 
0.602921 
0.634928 
0.666493 
0.697591 
0.728194 
0.758276 
0.787812 
0.816777 
0.845146 
0.872896 
0.900003 
0.926445 
0.952199 
0.977244 
1.00156 
1.02513 
1.04793 
1.06994 
1.09115 
0.155437 
0.19157 
0.227671 
0.263712 
0.299661 
0.335489 
0.371165 
0.406658 
0.44194 
0.47698 
0.511749 
0.546219 
0.580359 
0.614141 
0.647538 
0.680521 
0.713063 
0.745137 
0.776716 
0.807775 
0.838288 
0.868229 
0.897575 
0.926301 
0.954384 
0.981802 
1.00853 
1.03455 
1.05985 
1.08439 
1.10817 
1.13115 
1.15334 
0.186229 
0.223338 
0.260417 
0.297434 
0.33436 
0.371164 
0.407816 
0.444287 
0.480545 
0.516562 
0.552308 
0.587753 
0.62287 
0.657629 
0.692002 
0.725962 
0.759481 
0.792531 
0.825087 
0.857122 
0.888611 
0.919529 
0.949851 
0.979554 
1.00861 
1.03701 
1.06471 
1.09171 
1.11798 
1.1435 
1.16825 
1.19222 
1.21537 
0.216839 
0.254924 
0.29298 
0.330974 
0.368876 
0.406657 
0.444286 
0.481733 
0.518968 
0.555961 
0.592684 
0.629106 
0.665199 
0.700935 
0.736285 
0.771221 
0.805716 
0.839743 
0.873275 
0.906287 
0.938752 
0.970647 
1.00195 
1.03262 
1.06266 
1.09203 
1.12071 
1.14869 
1.17593 
1.20243 
1.22816 
1.2531 
1.27723 
0.247237 
0.286299 
0.325331 
0.364302 
0.403181 
0.441939 
0.480544 
0.518968 
0.557179 
0.595149 
0.632848 
0.670247 
0.707317 
0.744029 
0.780355 
0.816268 
0.851739 
0.886743 
0.921252 
0.95524 
0.988682 
1.02155 
1.05383 
1.08548 
1.1165 
1.14684 
1.1765 
1.20545 
1.23367 
1.26114 
1.28785 
1.31376 
1.33887 
0.277393 
0.317432 
0.357441 
0.397388 
0.437244 
0.476978 
0.51656 
0.55596 
0.595149 
0.634095 
0.672771 
0.711146 
0.749192 
0.786881 
0.824184 
0.861073 
0.897521 
0.933501 
0.968986 
1.00395 
1.03837 
1.07222 
1.10547 
1.1381 
1.17009 
1.20141 
1.23205 
1.26197 
1.29117 
1.31962 
1.3473 
1.37419 
1.40028 
0.307279 
0.348295 
0.38928 
0.430204 
0.471036 
0.511747 
0.552305 
0.592682 
0.632847 
0.67277 
0.712422 
0.751774 
0.790797 
0.829462 
0.867741 
0.905607 
0.943031 
0.979988 
1.01645 
1.05239 
1.08779 
1.12261 
1.15684 
1.19044 
1.22341 
1.25571 
1.28732 
1.31822 
1.3484 
1.37782 
1.40648 
1.43435 
1.46141 
0.336865 
0.378857 
0.420818 
0.462719 
0.504528 
0.546215 
0.58775 
0.629104 
0.670245 
0.711145 
0.751773 
0.792102 
0.832101 
0.871743 
0.910999 
0.949841 
0.988242 
1.02617 
1.06361 
1.10053 
1.1369 
1.1727 
1.20791 
1.24249 
1.27643 
1.30971 
1.3423 
1.37418 
1.40532 
1.43573 
1.46536 
1.4942 
1.52224 
0.366121 
0.40909 
0.452028 
0.494905 
0.537691 
0.580354 
0.622866 
0.665196 
0.707314 
0.74919 
0.790795 
0.8321 
0.873076 
0.913694 
0.953927 
0.993745 
1.03312 
1.07203 
1.11045 
1.14834 
1.18569 
1.22246 
1.25864 
1.29421 
1.32912 
1.36338 
1.39694 
1.4298 
1.46192 
1.4933 
1.52391 
1.55373 
1.58274 
0.39502 
0.438965 
0.48288 
0.526734 
0.570496 
0.614136 
0.657624 
0.700931 
0.744025 
0.786878 
0.82946 
0.871741 
0.913693 
0.955288 
0.996497 
1.03729 
1.07765 
1.11753 
1.15692 
1.19579 
1.23412 
1.27187 
1.30903 
1.34556 
1.38146 
1.41669 
1.45123 
1.48506 
1.51816 
1.55052 
1.5821 
1.6129 
1.64289 
0.423533 
0.468455 
0.513346 
0.558176 
0.602915 
0.647532 
0.691997 
0.73628 
0.780351 
0.82418 
0.867738 
0.910996 
0.953925 
0.996496 
1.03868 
1.08045 
1.12178 
1.16265 
1.20301 
1.24286 
1.28216 
1.32089 
1.35902 
1.39654 
1.43341 
1.46961 
1.50513 
1.53994 
1.57402 
1.60735 
1.63991 
1.67168 
1.70265 
0.451632 
0.497531 
0.543398 
0.589205 
0.63492 
0.680514 
0.725955 
0.771215 
0.816262 
0.861068 
0.905603 
0.949837 
0.993743 
1.03729 
1.08045 
1.1232 
1.16551 
1.20735 
1.24869 
1.28951 
1.32979 
1.36949 
1.4086 
1.44709 
1.48494 
1.52212 
1.55862 
1.5944 
1.62946 
1.66376 
1.6973 
1.73005 
1.76199 
0.47929 
0.526165 
0.57301 
0.619793 
0.666485 
0.713055 
0.759473 
0.805709 
0.851733 
0.897515 
0.943026 
0.988237 
1.03312 
1.07764 
1.12178 
1.16551 
1.20879 
1.2516 
1.29392 
1.33572 
1.37698 
1.41766 
1.45775 
1.49721 
1.53604 
1.57419 
1.61166 
1.64842 
1.68446 
1.71974 
1.75425 
1.78798 
1.8209 
0.50648 
0.554332 
0.602153 
0.649913 
0.697581 
0.745128 
0.792522 
0.839735 
0.886735 
0.933494 
0.979982 
1.02617 
1.07203 
1.11753 
1.16264 
1.20734 
1.2516 
1.29539 
1.33869 
1.38147 
1.4237 
1.46536 
1.50642 
1.54686 
1.58666 
1.62579 
1.66424 
1.70198 
1.73899 
1.77524 
1.81073 
1.84544 
1.87933 
0.533176 
0.582004 
0.630801 
0.679538 
0.728183 
0.776706 
0.825077 
0.873266 
0.921243 
0.968978 
1.01644 
1.06361 
1.11044 
1.15692 
1.20301 
1.24869 
1.29392 
1.33869 
1.38296 
1.42672 
1.46992 
1.51256 
1.5546 
1.59602 
1.63679 
1.6769 
1.71632 
1.75504 
1.79302 
1.83026 
1.86672 
1.9024 
1.93727 
0.559351 
0.609155 
0.658929 
0.708642 
0.758264 
0.807763 
0.857111 
0.906276 
0.95523 
1.00394 
1.05238 
1.10052 
1.14833 
1.19579 
1.24286 
1.28951 
1.33572 
1.38147 
1.42672 
1.47144 
1.51563 
1.55924 
1.60225 
1.64465 
1.6864 
1.72749 
1.76789 
1.80758 
1.84654 
1.88475 
1.92219 
1.95884 
1.99469 
0.584979 
0.63576 
0.686511 
0.7372 
0.787798 
0.838274 
0.888598 
0.93874 
0.98867 
1.03836 
1.08778 
1.13689 
1.18568 
1.23411 
1.28215 
1.32978 
1.37697 
1.42369 
1.46992 
1.51563 
1.56078 
1.60537 
1.64936 
1.69274 
1.73546 
1.77753 
1.8189 
1.85957 
1.89951 
1.93869 
1.97711 
2.01474 
2.05157 
0.610036 
0.661794 
0.713521 
0.765187 
0.816762 
0.868214 
0.919515 
0.970633 
1.02154 
1.0722 
1.1226 
1.17269 
1.22246 
1.27186 
1.32088 
1.36949 
1.41765 
1.46535 
1.51255 
1.55924 
1.60537 
1.65094 
1.6959 
1.74025 
1.78396 
1.827 
1.86935 
1.91099 
1.9519 
1.99207 
2.03146 
2.07007 
2.10787 
0.634498 
0.687232 
0.739936 
0.792578 
0.845129 
0.897558 
0.949835 
1.00193 
1.05381 
1.10545 
1.15682 
1.20789 
1.25863 
1.30902 
1.35901 
1.4086 
1.45774 
1.50641 
1.55459 
1.60225 
1.64936 
1.6959 
1.74185 
1.78717 
1.83185 
1.87587 
1.9192 
1.96182 
2.00371 
2.04484 
2.08522 
2.1248 
2.16358 
0.65834 
0.71205 
0.765731 
0.81935 
0.872877 
0.926283 
0.979536 
1.03261 
1.08547 
1.13808 
1.19043 
1.24248 
1.29419 
1.34555 
1.39653 
1.44709 
1.49721 
1.54686 
1.59601 
1.64465 
1.69273 
1.74025 
1.78717 
1.83347 
1.87913 
1.92412 
1.96843 
2.01202 
2.05489 
2.097 
2.13835 
2.17891 
2.21867 
0.681539 
0.736226 
0.790883 
0.845478 
0.899982 
0.954364 
1.00859 
1.06264 
1.11648 
1.17007 
1.22339 
1.27642 
1.32911 
1.38145 
1.4334 
1.48493 
1.53603 
1.58665 
1.63679 
1.6864 
1.73546 
1.78395 
1.83185 
1.87913 
1.92576 
1.97173 
2.01701 
2.06158 
2.10543 
2.14852 
2.19084 
2.23238 
2.27311 
0.704072 
0.759736 
0.815369 
0.870941 
0.926422 
0.98178 
1.03699 
1.09201 
1.14682 
1.20139 
1.25569 
1.30969 
1.36336 
1.41667 
1.4696 
1.52211 
1.57418 
1.62579 
1.6769 
1.72748 
1.77752 
1.82699 
1.87587 
1.92412 
1.97173 
2.01868 
2.06493 
2.11048 
2.1553 
2.19937 
2.24267 
2.28518 
2.32689 
0.725918 
0.782559 
0.839168 
0.895717 
0.952174 
1.00851 
1.06469 
1.12069 
1.17648 
1.23203 
1.2873 
1.34228 
1.39693 
1.45121 
1.50512 
1.55861 
1.61165 
1.66423 
1.71632 
1.76788 
1.8189 
1.86935 
1.9192 
1.96843 
2.01701 
2.06493 
2.11217 
2.15869 
2.20449 
2.24953 
2.29381 
2.3373 
2.37998 
0.747056 
0.804673 
0.862259 
0.919784 
0.977217 
1.03453 
1.09169 
1.14866 
1.20543 
1.26195 
1.31821 
1.37416 
1.42978 
1.48505 
1.53992 
1.59439 
1.64841 
1.70197 
1.75503 
1.80757 
1.85957 
1.91099 
1.96181 
2.01202 
2.06158 
2.11048 
2.15869 
2.20619 
2.25296 
2.29898 
2.34424 
2.3887 
2.43236 
0.767464 
0.826057 
0.88462 
0.943121 
1.00153 
1.05982 
1.11795 
1.17591 
1.23365 
1.29115 
1.34838 
1.40531 
1.46191 
1.51815 
1.574 
1.62944 
1.68445 
1.73898 
1.79302 
1.84653 
1.8995 
1.9519 
2.0037 
2.05489 
2.10543 
2.1553 
2.20449 
2.25296 
2.30071 
2.34771 
2.39394 
2.43938 
2.48401 
0.787123 
0.846693 
0.906232 
0.965709 
1.02509 
1.08436 
1.14347 
1.2024 
1.26112 
1.31959 
1.3778 
1.4357 
1.49328 
1.5505 
1.60733 
1.66375 
1.71973 
1.77524 
1.83025 
1.88474 
1.93869 
1.99206 
2.04484 
2.097 
2.14852 
2.19937 
2.24953 
2.29899 
2.34771 
2.39568 
2.44289 
2.48931 
2.53492 
0.806015 
0.866561 
0.927075 
0.987528 
1.04789 
1.10813 
1.16822 
1.22812 
1.28782 
1.34727 
1.40645 
1.46534 
1.52389 
1.58208 
1.63989 
1.69729 
1.75424 
1.81072 
1.86671 
1.92218 
1.97711 
2.03146 
2.08522 
2.13835 
2.19084 
2.24267 
2.29381 
2.34424 
2.39394 
2.44289 
2.49107 
2.53846 
2.58505 
0.824122 
0.885642 
0.947131 
1.00856 
1.0699 
1.13111 
1.19218 
1.25306 
1.31373 
1.37416 
1.43432 
1.49418 
1.55371 
1.61288 
1.67166 
1.73003 
1.78796 
1.84543 
1.90239 
1.95884 
2.01474 
2.07007 
2.1248 
2.17891 
2.23238 
2.28518 
2.3373 
2.38871 
2.43938 
2.48931 
2.53847 
2.58684 
2.6344 
0.841431 
0.903919 
0.966382 
1.02879 
1.0911 
1.15329 
1.21534 
1.27719 
1.33884 
1.40025 
1.46138 
1.52222 
1.58272 
1.64287 
1.70263 
1.76198 
1.82089 
1.87932 
1.93727 
1.99469 
2.05157 
2.10787 
2.16358 
2.21867 
2.27311 
2.32689 
2.37999 
2.43237 
2.48402 
2.53492 
2.58506 
2.6344 
2.68294 
];
figure(1);
plot3(X(:,1),X(:,2),V, '.');
hold on;
R = [
-0.287554
-1.6214
-2.89976
-4.16881
-5.44839
-6.58325
-7.36783
-8.12969
-8.86843
-9.58544
-10.2831
-10.964
-11.6312
-12.287
-12.9338
-13.5736
-14.2079
-14.838
-15.4648
-16.0891
-16.7116
-17.3327
-17.9527
-18.5719
-19.1906
-19.8087
-20.4266
-21.0442
-21.6615
-22.2788
-22.896
-23.513
-24.13
-24.747
-25.364
];
figure(2);
subplot(4,1,4);
plot(R,'.');
title('Residual: n = 32');
figure(1);
legend('4', '8', '16', '32');
saveas(gcf,'oneSolutionInd9.png');
clf
figure(2);
saveas(gcf,'oneResidualInd9.png');

N = [
4
8
16
32
];
E = [
-7.17394
-9.09022
-10.6215
-12.3939
];
figure(3);
plot(log2(N),E,'-', 'MarkerSize', 5);
hold on;

T1 = [
2.1e-05
0.00023
0.006077
0.361483
];
T2 = [
0.002205
0.026701
0.344255
4.85129
];
figure(4);
subplot(3,1,3);
plot(N,T1, '-', 'MarkerSize', 5);
hold on;
plot(N,T2, '-', 'MarkerSize', 5);
legend('Lapcak', 'Multigrid');
ylabel('time(s)');
xlabel('n');

figure(3);
title('Convergence rates');
legend('Dirichlet', 'Neumann', 'Mixed');
xlabel('log n');
ylabel('log of error');
saveas(gcf,'oneErrorInd3.png');
clf;
figure(4);
subplot(3,1,1);
title('Dirichlet');
subplot(3,1,2);
title('Neumann');
subplot(3,1,3);
title('Mixed');
saveas(gcf,'oneTimeInd3.png');
clf;
